[{"data":1,"prerenderedAt":1001},["ShallowReactive",2],{"layer:electricity:understand":3},{"layer":4,"contentHash":980,"dependencyHashes":981,"approval":994,"releaseId":1000},{"schemaVersion":5,"conceptId":6,"locale":7,"depth":8,"revision":5,"title":9,"subtitle":10,"summary":11,"objectives":12,"estimatedMinutes":18,"plate":19,"blocks":40,"sourceIds":975,"reviewStatus":976,"authoring":977},1,"electricity","en","understand","The big three: voltage, current, resistance","The push, the flow and the pushback, and the one rule that ties them together","Build the pump-and-pipe picture of a circuit, then meet voltage (the push), current (the flow) and resistance (the pushback) with real numbers from AA cells to lightning. Finish with Ohm's law, V = I × R, and the mix-ups it clears up.",[13,14,15,16,17],"Describe voltage, current and resistance in your own words and match each to part of the water-and-pump picture.","Place everyday voltages, currents and resistances on a scale, from an LED to lightning.","Read a charger's rating plate and explain what each number and symbol means.","Use V = I × R and its rearrangements to calculate any one quantity from the other two.","Explain why current is not used up, why batteries do not store current, and why wet skin is so much more dangerous than dry skin.",35,{"title":20,"rows":21},"Lesson plate",[22,25,28,31,34,37],{"label":23,"value":24},"Depth","Understand",{"label":26,"value":27},"Reading time","≈ 35 minutes",{"label":29,"value":30},"Prior knowledge","A circuit is a complete loop (Discover)",{"label":32,"value":33},"Chapters","10",{"label":35,"value":36},"Labs","Ohm's law lab, body-current lab, device explorer",{"label":38,"value":39},"Units used","V, A, mA, Ω, W",[41,45,51,57,60,66,72,77,82,88,117,120,125,130,169,172,186,191,194,199,236,244,269,274,280,303,308,341,344,350,354,372,377,383,406,427,432,460,463,466,471,474,487,491,503,512,520,524,540,573,576,584,596,609,614,617,678,683,688,691,702,706,721,745,750,753,758,762,766,770,794,799,802,806,810,944,964],{"id":42,"type":43,"markdown":44},"intro-three-numbers","prose","Pick up any phone charger and turn it over. Somewhere in the tiny grey print you will find numbers like **5 V** and **2 A**. Look at the sticker under a kettle and you will see **230 V**. Ask an electrician why a wire got hot and you will hear the word **resistance**.\n\nThose three ideas, **voltage**, **current** and **resistance**, are the whole grammar of electricity. Every circuit in your home, from a torch to a geyser to the metro, is a story about how hard charge is being pushed, how much of it flows, and what is pushing back.\n\nIn this layer you will build one clear mental picture, give each of the three a proper name and unit, meet real numbers for each (from a single LED to a bolt of lightning), and then join them with the most useful rule in all of electricity: **V = I × R**.",{"id":46,"type":47,"variant":48,"title":49,"markdown":50},"intro-how-to-read","callout","observation","How to use this lesson","Each chapter builds on the last, so read in order the first time. Use the chapter menu to jump back later. Whenever you see a **prediction**, commit to an answer before you read on: being surprised is how the idea sticks.",{"id":52,"type":53,"title":54,"eyebrow":55,"navLabel":56},"ch1","chapter","A picture you can carry in your head","Chapter 01","1 The water picture",{"id":58,"type":43,"markdown":59},"water-picture-prose","You cannot see electrons moving in a wire, so we borrow a picture of something we *can* see: **water in a closed loop of pipes, driven by a pump**.\n\nImagine a small pump sitting in a ring of pipe that is already completely full of water. Switch the pump on and it pushes. Water starts moving everywhere in the loop at once: past the pump, along the pipe, through a narrow section and back to the pump again. Nothing is poured in and nothing leaks out. The same water just goes round and round.\n\nNow swap the words:\n\n- The **pump** is the battery or the socket. It provides the **push**. That push is **voltage**.\n- The **water** is electric charge, mostly electrons that were *already sitting in the metal* before you switched anything on.\n- How much water passes a point each second is the **flow**. That flow is **current**.\n- A **narrow section of pipe** fights the flow. That is **resistance**, and in a real circuit it is the bulb filament, the heater coil or the motor.\n- The wide, smooth pipes are the **connecting wires**, which let charge through with very little fight.",{"id":61,"type":62,"diagram":63,"caption":64,"alt":65},"water-circuit-diagram","diagram","water-circuit","The water picture side by side with a real circuit: pump ↔ battery, pipe ↔ wire, narrow pipe ↔ bulb, flow rate ↔ current.","Two loops drawn side by side. On the left, a pump pushes water around a closed ring of pipe; one part of the pipe is narrow, and arrows show water flowing all the way round. On the right, a battery is connected by wires to a bulb in a single loop, with arrows showing current flowing round. Labels link the pump to the battery (voltage, the push), the wide pipe to the wire, the narrow pipe to the bulb (resistance), and the rate of water flow to the current.",{"id":67,"type":43,"markdown":68,"help":69},"rooftop-tank","If you live in a building with an **overhead tank**, you already know a second version of this picture. The higher the tank sits above your tap, the harder water gushes out. The *height difference* between tank and tap is what drives the flow, just as the voltage between the two ends of a circuit drives the current.\n\nNotice the words *difference* and *between*. A tank on the roof pushes water down to the ground floor, but a tank sitting on the ground floor next to your tap would push nothing, even if it held the same water. What matters is not how high the tank is in some absolute sense; it is how much higher it is than where the water is going. Hold on to that idea: it is the key to voltage in the next chapter.",{"simplerExplanation":70,"anotherExample":71},"Battery = pump (the push). Charge = water (already in the pipes). Current = how fast the water flows. Resistance = a narrow bit of pipe that slows the flow.","Think of a crowded metro platform emptying through a single narrow exit gate. The crowd pressing from behind is the voltage, the number of people squeezing through per second is the current, and the narrow gate is the resistance. Open a second gate and more people get through each second without anyone pushing harder.",{"id":73,"type":47,"variant":74,"title":75,"markdown":76},"water-model-limit","model_limit","Where the water picture breaks","The analogy is excellent for voltage, current and resistance, but do not stretch it too far.\n\n- Cut a water pipe and water sprays out. Cut a wire and the charge simply **stops**: electrons do not pour out of the cut end.\n- Individual electrons crawl along a wire astonishingly slowly, often less than a millimetre per second. Yet a bulb lights the instant you flick the switch, because the whole loop was already full of charge and the push travels round almost at once.\n- Water has weight and falls downhill. Charge does not care which way up a circuit is.",{"id":78,"type":53,"title":79,"eyebrow":80,"navLabel":81},"ch2","Voltage is the push","Chapter 02","2 Voltage",{"id":83,"type":43,"markdown":84,"help":85},"voltage-meaning","**Voltage** is how hard a source pushes charge around a circuit. More precisely, it measures **how much energy each bit of charge gains or loses** as it moves between two points.\n\nThe official unit is the **volt (V)**. One volt means one joule of energy for every coulomb of charge (a coulomb is a standard bundle of charge, about the amount carried by 6.24 × 10¹⁸ electrons). So:\n\n- An AA cell marked **1.5 V** gives every coulomb of charge that passes through it 1.5 joules of energy.\n- A **230 V** socket gives every coulomb 230 joules, over 150 times as much.\n\nThat is why a socket can boil water and an AA cell cannot: each packet of charge arrives carrying far more energy.",{"simplerExplanation":86,"anotherExample":87},"Voltage is the strength of the push. A bigger voltage means each bit of charge is pushed harder and carries more energy to whatever it passes through.","Imagine delivery riders each carrying a bag of food. Voltage is like how full each bag is. 1.5 V means small bags; 230 V means enormous bags. The number of riders passing per second is a different question entirely (that is current).",{"id":89,"type":90,"tone":91,"items":92},"voltage-spec","spec","amber",[93,97,101,105,109,113],{"label":94,"big":95,"value":96},"Symbol","V","Written V in formulas (some books use ΔV, “the change in V”).",{"label":98,"big":99,"value":100},"Unit","volt","Also written V. 1 V = 1 joule per coulomb. 1 kV = 1,000 V.",{"label":102,"big":103,"value":104},"Named after","Volta","Alessandro Volta, whose stacked zinc–copper “pile” of 1800 was the first battery.",{"label":106,"big":107,"value":108},"Water picture","Pressure","The pressure difference the pump creates, or the height of the rooftop tank above the tap.",{"label":110,"big":111,"value":112},"Measured with","Voltmeter","Connected **across** a part: one probe on each side of it.",{"label":114,"big":115,"value":116},"Always","Between","A voltage is always *between two points*. “The voltage at one point” only makes sense compared with somewhere else.",{"id":118,"type":43,"markdown":119},"voltage-between","That last card is the one most people miss. **Voltage is always between two points.**\n\nWhen we say “the socket is 230 V”, we really mean the live pin is 230 V different from the neutral pin (which is kept close to the voltage of the earth under your feet). When we say “an AA cell is 1.5 V”, we mean its **+** end is 1.5 V above its **−** end.\n\nThis is why a voltmeter always has **two** probes. You touch one to each side of the thing you are measuring, and it tells you the difference. A voltmeter with one probe dangling in the air reads nothing useful at all, just as a single tank on its own tells you nothing about how hard water will gush from a tap.",{"id":121,"type":47,"variant":122,"title":123,"markdown":124},"bird-aha","aha","Why birds can sit on power lines","A pigeon perched on a single overhead wire carrying thousands of volts is perfectly comfortable. Both of its feet are on the **same wire**, at practically the same voltage, so there is almost no voltage *between* its feet and almost no current flows through it.\n\nThe danger comes when something touches two points at different voltages at once: the wire *and* a pole, the wire *and* the ground, or two different wires. That is exactly what happens when a person touches a line from a ladder or a rooftop.",{"id":126,"type":47,"variant":127,"title":128,"markdown":129},"bird-careful","careful","Never test this","Overhead lines, transformer boxes and railway wires can kill without being touched: at very high voltages the current can jump through the air to a nearby hand, rod or kite string. Stay well away, never fly kites or climb near lines, and never touch a fallen wire. The bird story explains an idea. It is not a safety rule for people.",{"id":131,"type":132,"title":133,"note":134,"scale":135,"rungs":136},"voltage-ladder","ladder","Voltages from your pocket to the sky","Log scale: each step up the ladder is roughly ten times or more the one below. Values are typical, not exact.","log",[137,141,145,149,153,157,161,165],{"label":138,"value":139,"display":140},"AA or AAA cell",1.5,"1.5 V",{"label":142,"value":143,"display":144},"USB port \u002F phone charger output",5,"5 V",{"label":146,"value":147,"display":148},"Car or bike battery",12,"12 V",{"label":150,"value":151,"display":152},"Laptop charger output",20,"≈ 20 V",{"label":154,"value":155,"display":156},"Home socket in India",230,"230 V",{"label":158,"value":159,"display":160},"Railway and metro overhead wire",25000,"25,000 V (25 kV)",{"label":162,"value":163,"display":164},"Long-distance transmission line",400000,"400,000 V (400 kV)",{"label":166,"value":167,"display":168},"Lightning bolt",100000000,"≈ 100 million V or more",{"id":170,"type":43,"markdown":171},"voltage-ladder-notes","A few things jump out from that ladder.\n\n- The **socket in your wall** pushes about **150 times** harder than an AA cell (230 ÷ 1.5 ≈ 153). This is why battery experiments are safe to do and socket experiments are not.\n- Homes in the USA use about **120 V**, roughly half of India's 230 V. Most of Europe, the UK and Australia use 230 V, like India.\n- Electric trains on Indian Railways and most metro systems take **25 kV** from the overhead wire, over a hundred times the push of a home socket.\n- The big steel towers striding across fields often carry **400 kV** or more (India also runs 765 kV lines). Later layers explain why the grid uses such enormous voltages.\n- Lightning has no neat single value. Estimates range from about 100 million to a billion volts between cloud and ground.",{"id":173,"type":174,"itemId":175,"prompt":176,"check":177,"hints":181,"feedback":183},"voltage-practice","practice","electricity.understand-voltage-two-cells","A torch holds two AA cells, each 1.5 V, placed end to end (+ of one touching − of the next). What is the total voltage pushing current through the bulb?",{"kind":178,"answer":179,"tolerance":180,"unit":95},"number",3,0,[182],"Cells stacked end to end add their pushes together, like two pumps one after the other.",{"correct":184,"incorrect":185},"Right: 1.5 V + 1.5 V = 3 V. Stacking cells in a line (in series) adds their voltages. Four AA cells would give 6 V.","Cells placed end to end add their voltages: 1.5 V + 1.5 V = 3 V. It is like placing two pumps one after the other in the same pipe.",{"id":187,"type":53,"title":188,"eyebrow":189,"navLabel":190},"ch3","Reading a charger's rating plate","Chapter 03","3 The rating plate",{"id":192,"type":43,"markdown":193},"plate-intro","Every electrical device sold legally carries a **rating plate**: a sticker or moulded label listing what it expects to be fed and what it gives out. Engineers read these the way doctors read a prescription. Once you can read one, a phone charger stops being a mystery box.\n\nHere is what a typical phone charger says (the wording varies slightly between brands):",{"id":195,"type":47,"variant":196,"title":197,"markdown":198},"plate-try","try_it","Find a charger and read it","Unplug a phone charger (switch off at the socket first) and look for tiny print on its side. You are likely to find something like:\n\n**INPUT: 100–240 V ~ 50\u002F60 Hz 0.3 A**\n\n**OUTPUT: 5 V ⎓ 2 A**\n\nCopy down what yours says. Then check it against the table below. If you have a laptop charger, compare the two: the laptop one will usually have a higher output voltage (around 19–20 V) and a much bigger output in watts.",{"id":200,"type":201,"caption":202,"columns":203,"rows":207},"plate-table","table","What each part of a charger's rating plate means",[204,205,206],"On the plate","What it means","Why it matters",[208,212,216,220,224,228,232],[209,210,211],"**INPUT 100–240 V**","It can be fed any mains voltage from 100 V to 240 V.","The same charger works in India (230 V), the USA (120 V) and Japan (100 V). Only the plug shape may need an adapter.",[213,214,215],"**~**","A wavy line means **AC**, alternating current: the push reverses direction many times a second.","Mains electricity in every country is AC. Later layers explain why.",[217,218,219],"**50\u002F60 Hz**","The number of back-and-forth cycles each second that it accepts.","India uses 50 Hz; the USA uses 60 Hz. This charger is happy with either.",[221,222,223],"**0.3 A** (input)","The most current it may draw from the socket, usually when running on the lowest input voltage.","Tiny compared with a kettle. Typical charging draws much less.",[225,226,227],"**OUTPUT 5 V**","The push it gives your phone.","This matches the USB standard. Feeding a phone 230 V directly would destroy it.",[229,230,231],"**⎓**","A solid line over a dashed line means **DC**, direct current: the push is always in one direction.","Batteries, phones and laptops all run on DC.",[233,234,235],"**2 A** (output)","The most current it can safely supply at 5 V.","Your phone decides how much it actually takes, up to this limit.",{"id":237,"type":43,"markdown":238,"help":239},"plate-power","Two quick things you can already work out from the plate.\n\n**First, the charger is a voltage changer.** It takes 230 V AC from the wall and turns it into 5 V DC, about 46 times less push (230 ÷ 5 = 46). Inside is a small transformer and some electronics; later layers open one up.\n\n**Second, you can find its power.** Multiply volts by amps: 5 V × 2 A = **10 W**. You will meet this rule properly in the last chapter. For now, notice that a fast charger marked **9 V ⎓ 2 A** gives 18 W, nearly twice as much, which is exactly why it fills your battery faster.",{"simplerExplanation":240,"hints":241},"~ means AC (the push flips back and forth). ⎓ means DC (the push goes one way). The charger takes in big-push AC from the wall and gives out small-push DC to the phone.",[242,243],"Look for the word INPUT: that is what comes from the wall.","Look for the word OUTPUT: that is what goes to the phone.",{"id":245,"type":174,"itemId":246,"prompt":247,"check":248,"hints":264,"feedback":266},"plate-practice","electricity.understand-plate-dc-symbol","On a charger's plate, the output line reads **5 V ⎓ 2 A**. What does the symbol ⎓ tell you?",{"kind":249,"options":250,"correct":263},"choice",[251,254,257,260],{"id":252,"label":253},"dc","The output is DC: the push is always in one direction.",{"id":255,"label":256},"ac","The output is AC: the push reverses many times a second.",{"id":258,"label":259},"earth","The charger must be connected to an earth wire.",{"id":261,"label":262},"fuse","The charger contains a 2 A fuse.",[252],[265],"One of the symbols is wavy and one is straight. Which kind of push is steady?",{"correct":267,"incorrect":268},"Yes. The straight line (with a dashed line under it) means direct current. The wavy ~ on the input side means alternating current.","⎓ means DC, a push that stays in one direction, which is what phone batteries need. The wavy ~ means AC, which is what the wall socket supplies.",{"id":270,"type":53,"title":271,"eyebrow":272,"navLabel":273},"ch4","Current is the flow","Chapter 04","4 Current",{"id":275,"type":43,"markdown":276,"help":277},"current-meaning","**Current** is **how much charge passes a point each second**. In the water picture it is the flow rate: litres per second through a pipe.\n\nThe unit is the **ampere**, usually shortened to **amp (A)**. One amp means one coulomb of charge passing a point every second. Since a coulomb is about 6.24 × 10¹⁸ electrons, that is:\n\n**1 A ≈ 6,240,000,000,000,000,000 electrons passing every second.**\n\nSix and a quarter billion billion. If you tried to count them at one per second, you would need about 200 billion years for a single second's worth, over ten times the age of the universe.\n\nSmaller currents are measured in **milliamps (mA)**: 1 mA is one thousandth of an amp, so 1,000 mA = 1 A.",{"simplerExplanation":278,"anotherExample":279},"Current is the amount of flow: how much charge goes past a point in one second. Bigger current = more charge rushing past.","Standing at a toll plaza, you could count cars per minute. That count is like current. It says nothing about how fast each car is going or how heavy it is, only how many go past per unit of time.",{"id":281,"type":90,"tone":282,"items":283},"current-spec","blue",[284,287,290,293,296,299],{"label":94,"big":285,"value":286},"I","From the French *intensité de courant*, “intensity of current”.",{"label":98,"big":288,"value":289},"ampere","Written A. 1 A = 1 coulomb per second. 1 mA = 0.001 A.",{"label":102,"big":291,"value":292},"Ampère","André-Marie Ampère (1775–1836), a French physicist who showed that currents push and pull on each other magnetically.",{"label":106,"big":294,"value":295},"Flow rate","Litres of water passing a point in the pipe each second.",{"label":110,"big":297,"value":298},"Ammeter","Connected **in line** (in series): the current has to flow *through* the meter to be counted.",{"label":300,"big":301,"value":302},"Key fact","Same all round","In a single loop, the current is the same at every point. None is used up on the way.",{"id":304,"type":47,"variant":305,"title":306,"markdown":307},"meters-compare","definition","Across versus through","A **voltmeter** goes **across** a part, like a pressure gauge with one tube before a narrow pipe and one after it. An **ammeter** goes **in line**, like a flow meter cut into the pipe so all the water must pass through it. Mixing them up is the most common mistake in school labs, so say it out loud: *voltage across, current through*.",{"id":309,"type":132,"title":310,"note":311,"scale":135,"rungs":312},"current-ladder","Currents from a tiny light to a thunderbolt","Log scale. Appliance values are typical for Indian 230 V models while running.",[313,317,321,325,329,333,337],{"label":314,"value":315,"display":316},"Indicator LED",0.02,"20 mA (0.02 A)",{"label":318,"value":319,"display":320},"Ceiling fan (≈ 75 W)",0.3,"≈ 0.3 A",{"label":322,"value":323,"display":324},"Phone charging at 5 V",2,"≈ 2 A",{"label":326,"value":327,"display":328},"1.5 kW electric kettle",6.5,"≈ 6.5 A",{"label":330,"value":331,"display":332},"2 kW geyser",9,"≈ 9 A",{"label":334,"value":335,"display":336},"Car starter motor (while cranking)",200,"≈ 200 A",{"label":338,"value":339,"display":340},"Typical lightning stroke",30000,"≈ 30,000 A",{"id":342,"type":43,"markdown":343},"current-ladder-notes","Notice something odd? The **car starter motor** takes about **200 A**, far more than any appliance in your home, yet it runs from a humble **12 V** battery. And the phone takes **2 A** at only 5 V, while the ceiling fan takes a mere **0.3 A** at 230 V.\n\nBig voltage does not automatically mean big current, and small voltage does not mean small current. How much current flows depends on the push **and** on what is pushing back. That missing piece is resistance, and it arrives in the next chapter.",{"id":345,"type":43,"markdown":346,"help":347},"drawer-battery","Here is a puzzle. A fresh AA cell sitting in a kitchen drawer is **1.5 V**. How much current is flowing through it?\n\n**None at all.** There is a push, but nowhere for charge to go, because there is no complete loop. It is like a pump sitting in a shed with its pipes capped off: the pressure is there, ready and waiting, but no water moves.\n\nThis is the clearest way to see that voltage and current are **different things**. You can have voltage without current (the battery in the drawer, the socket with nothing plugged in). What you cannot have, in an ordinary circuit, is a steady current without a voltage pushing it.",{"simplerExplanation":348,"anotherExample":349},"Voltage is the push that is *available*. Current only flows when you give the charge a complete path to travel around.","A socket on the wall with nothing plugged in has 230 V between its holes all day and all night, but zero current flows, and your meter does not tick. Plug in a lamp and switch it on, and now there is a path, so current flows.",{"id":351,"type":47,"variant":122,"title":352,"markdown":353},"conventional-aha","The arrows point the “wrong” way","Circuit diagrams draw current flowing out of the **+** end of a battery, round the circuit, and into the **−** end. This is called **conventional current**.\n\nBut electrons carry *negative* charge, so in a metal wire they actually drift the other way: out of **−** and towards **+**.\n\nWhy the mismatch? In the 1700s, Benjamin Franklin and others had to guess which way “the electric fluid” moved, and they picked + to −. Electrons were not discovered until 1897. By then the convention was in every book and on every diagram, and it gives the same answers for almost every calculation, so it stayed. Physicists still use it today. Just remember: **conventional current + → −, electrons − → +**.",{"id":355,"type":356,"prompt":357,"options":358,"explanation":371},"current-not-used-prediction","prediction","A battery lights a single bulb. You put one ammeter in the wire **before** the bulb and another in the wire **after** it. The first reads 0.30 A. What does the second read?",[359,362,365,368],{"id":360,"label":361},"more","More than 0.30 A",{"id":363,"label":364},"same","Exactly 0.30 A",{"id":366,"label":367},"less","Less than 0.30 A, because the bulb uses some up",{"id":369,"label":370},"zero","Zero, because the bulb uses it all","**Exactly 0.30 A.** Every electron that goes into the bulb comes out the other side; there is nowhere else for it to go. The bulb takes **energy** from the charge (turning it into light and heat), but it does not destroy the charge itself. In the water picture, a water wheel takes energy from the flow, yet the same number of litres per second leaves the wheel as enters it. We will return to this in the mix-ups chapter, because almost everyone believes the opposite at first.",{"id":373,"type":53,"title":374,"eyebrow":375,"navLabel":376},"ch5","Resistance is what pushes back","Chapter 05","5 Resistance",{"id":378,"type":43,"markdown":379,"help":380},"resistance-meaning","**Resistance** is how strongly something **opposes the flow of current**. In the water picture it is a narrow, rough or clogged section of pipe.\n\nInside a metal, the drifting electrons keep bumping into the vibrating atoms of the material. Every bump slows them down and hands over a little energy, which shakes the atoms harder: the metal **warms up**. A material where electrons bump a lot has high resistance; a material where they slip through easily has low resistance.\n\nThe unit is the **ohm**, written with the Greek letter omega, **Ω**. A part has a resistance of 1 Ω if a push of 1 V drives a current of 1 A through it.",{"simplerExplanation":381,"anotherExample":382},"Resistance is how hard it is for current to get through something. Low resistance: easy path. High resistance: hard path.","Drinking a milkshake through a wide straw is easy; through a thin coffee stirrer it is hard work. Suck with the same strength (same voltage) and far less comes through the thin one (less current). The thin stirrer has more resistance.",{"id":384,"type":90,"tone":385,"items":386},"resistance-spec","copper",[387,390,393,396,399,402],{"label":94,"big":388,"value":389},"R","R for resistance.",{"label":98,"big":391,"value":392},"ohm (Ω)","1 Ω = 1 volt per amp. 1 kΩ = 1,000 Ω; 1 MΩ = 1,000,000 Ω.",{"label":102,"big":394,"value":395},"Ohm","Georg Simon Ohm, a German schoolteacher who published the rule linking V, I and R in 1827.",{"label":106,"big":397,"value":398},"Narrow pipe","A tight, long or clogged section that makes the pump work to get water through.",{"label":110,"big":400,"value":401},"Ohmmeter","Usually one setting on a multimeter, used on a part that is **disconnected** from any power.",{"label":403,"big":404,"value":405},"Side effect","Heat","Wherever current meets resistance, some electrical energy becomes heat.",{"id":407,"type":408,"title":409,"items":410},"resistance-factors","steps","Four things that set a wire's resistance",[411,415,419,423],{"title":412,"tag":413,"text":414},"Material","What it's made of","Copper and aluminium let electrons through easily. Nichrome, the alloy used in heater coils, resists about 60 times more than copper. Rubber, plastic and glass resist so much that we call them insulators.",{"title":416,"tag":417,"text":418},"Length","Longer = more","Double the length of a wire and you double its resistance: the electrons have twice as far to bump their way through. Like a pipe twice as long.",{"title":420,"tag":421,"text":422},"Thickness","Thicker = less","Double the cross-sectional area and you halve the resistance: there are twice as many lanes for charge to use. Like a wider pipe, or a wider road.",{"title":424,"tag":425,"text":426},"Temperature","Hotter = more (metals)","In metals, hotter atoms vibrate harder and get in the way more. A bulb filament's resistance when glowing is roughly ten to fifteen times its resistance when cold.",{"id":428,"type":47,"variant":429,"title":430,"markdown":431},"resistance-wiring-example","example","Why the geyser gets a thicker wire","In many Indian homes the lights are wired with **1.5 mm²** copper wire, ordinary sockets with **2.5 mm²**, and heavy loads like a geyser or air conditioner with **4 mm²** or thicker. A thicker wire has **less resistance**, so it wastes less energy as heat when a big current flows through it. Use a wire that is too thin for a big load and it runs hot, which can melt insulation and start a fire. The wire size is a safety decision, not a detail.",{"id":433,"type":132,"title":434,"note":435,"scale":135,"rungs":436},"resistance-ladder","Resistances from a copper wire to a rubber glove","Log scale. Body figures are rough illustrations; real skin resistance varies enormously with moisture, contact area and voltage.",[437,441,444,448,452,456],{"label":438,"value":439,"display":440},"1 m of 1 mm² copper wire",0.017,"≈ 0.017 Ω",{"label":442,"value":18,"display":443},"1.5 kW kettle element (hot)","≈ 35 Ω",{"label":445,"value":446,"display":447},"60 W bulb filament, glowing",880,"≈ 880 Ω",{"label":449,"value":450,"display":451},"Human body, wet skin",1000,"≈ 1,000 Ω",{"label":453,"value":454,"display":455},"Human body, dry skin",100000,"≈ 100,000 Ω",{"label":457,"value":458,"display":459},"Rubber electrician's glove",1000000000000,"> 10¹² Ω",{"id":461,"type":43,"markdown":462},"resistance-ladder-notes","Look at the spread: a metre of copper wire resists roughly **sixty million million times less** than a rubber glove (about 0.017 Ω versus more than 10¹² Ω). That colossal difference is the whole reason we can safely handle electrical things. We send current along copper and wrap it in plastic or rubber to keep it where it belongs.\n\nLook also at the **wet skin** and **dry skin** rungs. Water (especially sweaty, salty water) on your skin can cut your body's resistance by a factor of a hundred. Chapter 8 shows what that does to the current through you.",{"id":464,"type":43,"markdown":465},"resistance-useful","It is tempting to think of resistance as the villain, the thing that wastes energy. In connecting wires it mostly is. But in many devices, **resistance is the whole point**.\n\n- A **kettle**, **geyser**, **iron**, **toaster** or **room heater** contains a coil of high-resistance wire (usually nichrome). Current forced through it makes it hot. That heat is the product you paid for.\n- An old-style **filament bulb** has a tungsten wire so thin and so resistant that it heats to around 2,500 °C or more and glows white.\n- In electronics, small parts called **resistors** are added on purpose to limit current, for example to stop an LED from burning out.\n\nWhen you look at an appliance, ask: *where is the resistance, and is it the useful part or the wasteful part?*",{"id":467,"type":53,"title":468,"eyebrow":469,"navLabel":470},"ch6","Ohm's law: the rule that ties them together","Chapter 06","6 Ohm's law",{"id":472,"type":43,"markdown":473},"ohm-intro","You now have three quantities. Push (V), flow (I) and pushback (R). Georg Ohm's great discovery, published in 1827, was that for many materials they are linked by a beautifully simple rule:\n\n**voltage = current × resistance**, or **V = I × R**.\n\nRead it in the water picture: *to push a given flow through a narrow pipe, you need a pressure equal to the flow times the narrowness.* Or turn it round:\n\n- **Push harder** (more V) through the same resistance and **more current** flows. Double V, double I.\n- **Resist more** (more R) with the same push and **less current** flows. Double R, half I.\n\nThat is everything Ohm's law says. The three versions below are the same rule rearranged, so you can find whichever quantity is missing.",{"id":475,"type":476,"items":477},"ohm-formulas","formulas",[478,481,484],{"expression":479,"caption":480},"V = I × R","Find the voltage (V) when you know the current (A) and resistance (Ω).",{"expression":482,"caption":483},"I = V ÷ R","Find the current (A) from the push (V) and the pushback (Ω). The one you will use most.",{"expression":485,"caption":486},"R = V ÷ I","Find the resistance (Ω) by measuring the voltage across a part and the current through it.",{"id":488,"type":47,"variant":196,"title":489,"markdown":490},"ohm-triangle-tip","The cover-up triangle","Draw a triangle. Write **V** in the top half, and **I** and **R** side by side in the bottom half. Cover the one you want with your thumb:\n\n- Cover **V** and you see I next to R: **V = I × R**.\n- Cover **I** and you see V over R: **I = V ÷ R**.\n- Cover **R** and you see V over I: **R = V ÷ I**.\n\nIt is a memory aid, not a proof. Once you understand what each letter means, you will not need it.",{"id":492,"type":493,"title":494,"problem":495,"steps":496,"help":500},"we-torch","worked_example","A torch bulb on two AA cells","A torch runs on two AA cells (3 V in total). Its bulb has a resistance of 10 Ω. What current flows?",[497,498,499],"We know V = 3 V and R = 10 Ω. We want I, so use **I = V ÷ R**.","I = 3 ÷ 10 = **0.3 A**, which is 300 mA.","Sense check: small push, modest resistance, modest current. A torch drawing 0.3 A would drain a pair of ordinary AA cells in a few hours, which matches experience.",{"hints":501},[502],"Write down what you know with units, then pick the version of the formula that has your unknown on its own on the left.",{"id":504,"type":493,"title":505,"problem":506,"steps":507},"we-kettle","The resistance of a kettle element","A 1.5 kW kettle plugged into a 230 V socket draws about 6.5 A. What is the resistance of its heating element?",[508,509,510,511],"We know V = 230 V and I = 6.5 A. We want R, so use **R = V ÷ I**.","R = 230 ÷ 6.5 ≈ **35 Ω**.","Check by going back the other way: I = V ÷ R = 230 ÷ 35 ≈ 6.6 A. That matches the 6.5 A we started with (the tiny difference is rounding).","Notice how *small* 35 Ω is. A low resistance lets a big current through, and a big current through the element is what makes lots of heat quickly.",{"id":513,"type":493,"title":514,"problem":515,"steps":516},"we-geyser","A geyser's current","A 2 kW geyser's heating element has a resistance of about 26.5 Ω when hot. How much current does it draw from a 230 V supply?",[517,518,519],"Use **I = V ÷ R**.","I = 230 ÷ 26.5 ≈ **8.7 A**.","That is why the geyser in the current ladder shows about 9 A, and why it is usually wired on its own thicker cable with its own breaker.",{"id":521,"type":47,"variant":74,"title":522,"markdown":523},"ohm-model-limit","Ohm's law has conditions","V = I × R works perfectly for metal wires and resistors **kept at a steady temperature**. Many real things bend the rule:\n\n- A **filament bulb** heats up as current rises, so its resistance climbs. Its resistance cold is roughly a tenth to a fifteenth of its resistance glowing, which is why bulbs usually fail at the moment you switch them on.\n- **LEDs**, **diodes** and **batteries** do not have a fixed resistance at all.\n- **Skin** changes its resistance with moisture and even with the voltage applied.\n\nThe lab below uses a fixed resistance for each setting. That is a simplified model, and the numbers in this lesson are rounded.",{"id":525,"type":356,"prompt":526,"options":527,"explanation":539},"ohm-prediction","In the lab below, the torch bulb (10 Ω) is on 3 V and draws 0.3 A. You **double** the voltage to 6 V and leave the bulb the same. What happens to the current?",[528,531,533,536],{"id":529,"label":530},"half","It halves to 0.15 A",{"id":363,"label":532},"It stays at 0.3 A",{"id":534,"label":535},"double","It doubles to 0.6 A",{"id":537,"label":538},"four","It quadruples to 1.2 A","**It doubles to 0.6 A.** With R fixed, I = V ÷ R, so current is directly proportional to voltage: 6 ÷ 10 = 0.6 A. (A real filament would warm up and resist a bit more, so the actual rise would be slightly less than double. The lab uses the ideal model.)",{"id":541,"type":542,"component":543,"componentVersion":5,"config":544,"objective":566,"textAlternative":567,"help":568},"ohm-lab","interactive","ohms-law",{"voltage":545,"resistance":548,"fuseAmps":550,"presets":551},{"min":546,"max":547,"initial":179,"step":546},0.5,240,{"min":5,"max":450,"initial":549,"step":5},10,16,[552,554,557,559,561,564],{"label":553,"voltage":179,"resistance":549},"Torch bulb on 3 V",{"label":555,"voltage":331,"resistance":556},"Toy motor on 9 V battery",45,{"label":558,"voltage":155,"resistance":446},"60 W bulb on 230 V",{"label":560,"voltage":155,"resistance":18},"Kettle on 230 V",{"label":562,"voltage":155,"resistance":563},"Geyser on 230 V",26,{"label":565,"voltage":155,"resistance":323},"Fault: damaged cable, 230 V","See how current depends on both voltage and resistance, and find the point where a 16 A circuit breaker would trip.","The lab has a voltage slider (0.5 V to 240 V) and a resistance slider (1 Ω to 1,000 Ω). It shows the current I = V ÷ R and flags when the current is above 16 A, the rating of a typical socket-circuit MCB, which would trip and cut the supply. Preset results: torch bulb, 3 V across 10 Ω gives 0.3 A. Toy motor, 9 V across 45 Ω gives 0.2 A. A 60 W bulb, 230 V across 880 Ω gives about 0.26 A. Kettle, 230 V across 35 Ω gives about 6.6 A. Geyser, 230 V across 26 Ω gives about 8.8 A. All of these are safely below 16 A. A damaged cable whose wires touch might leave only about 2 Ω in the path: 230 ÷ 2 = 115 A, over seven times the breaker's limit, so it trips at once. At 230 V the breaker trips for any resistance below about 14.4 Ω, because 230 ÷ 16 ≈ 14.4. Doubling the voltage doubles the current; doubling the resistance halves it.",{"hints":569},[570,571,572],"Start with the torch preset, then double the voltage. Then return and double the resistance instead. Compare the two changes.","With the voltage at 230 V, slide the resistance down slowly. At what resistance does the breaker trip?","Try 12 V with resistance 1 Ω. Does a low voltage always mean a low current?",{"id":574,"type":43,"markdown":575},"mcb-prose","That last preset is how home safety devices do their job. In a **short circuit**, damaged insulation lets the live and neutral wires touch, leaving almost no resistance in the path. Ohm's law then says the current becomes enormous: 230 V across 2 Ω is **115 A**.\n\nA current like that would heat the house wiring dangerously within seconds. So every circuit in your distribution board is protected by a **miniature circuit breaker (MCB)** or, in older homes, a **fuse**: a deliberately weak link that breaks the circuit when the current goes above its rating. Typical ratings in Indian homes are 6 A or 10 A for lighting circuits and 16 A or more for power sockets and heavy appliances.\n\nThe MCB does not care about voltage directly. It watches **current**, because current is what heats wires.",{"id":577,"type":493,"title":578,"problem":579,"steps":580},"mcb-worked","Will the breaker trip?","A 16 A MCB protects a socket circuit on 230 V. A fault leaves a resistance of 4 Ω between live and neutral. Does the breaker trip?",[581,582,583],"Use **I = V ÷ R** = 230 ÷ 4 = **57.5 A**.","57.5 A is far above 16 A (more than three and a half times), so **yes, it trips**, cutting the supply before the wires overheat.","Compare with the kettle (35 Ω): 230 ÷ 35 ≈ 6.6 A, well under 16 A, so the breaker stays on. The same breaker tells a healthy appliance apart from a fault purely by the current.",{"id":585,"type":174,"itemId":586,"prompt":587,"check":588,"hints":590,"feedback":593},"ohm-practice-9v","electricity.understand-ohm-9v-450","A 9 V battery is connected across a 450 Ω resistor. What current flows, in **milliamps** (mA)?",{"kind":178,"answer":151,"tolerance":546,"unit":589},"mA",[591,592],"I = V ÷ R gives an answer in amps.","To turn amps into milliamps, multiply by 1,000.",{"correct":594,"incorrect":595},"Correct: 9 ÷ 450 = 0.02 A, which is 20 mA, exactly the current a typical indicator LED is designed for.","I = V ÷ R = 9 ÷ 450 = 0.02 A. Multiply by 1,000 to get milliamps: 20 mA.",{"id":597,"type":174,"itemId":598,"prompt":599,"check":600,"hints":604,"feedback":606},"ohm-practice-usb","electricity.understand-ohm-usb-resistance","A charger supplies 5 V and a phone is drawing 2 A from it. Treating the phone as a simple resistance, what is that resistance in ohms?",{"kind":178,"answer":601,"tolerance":602,"unit":603},2.5,0.05,"Ω",[605],"You know V and I and want R. Which version of Ohm's law puts R on its own?",{"correct":607,"incorrect":608},"Yes: R = V ÷ I = 5 ÷ 2 = 2.5 Ω. (A real phone's charging circuit adjusts itself as the battery fills, so this is only a snapshot.)","R = V ÷ I = 5 ÷ 2 = 2.5 Ω.",{"id":610,"type":53,"title":611,"eyebrow":612,"navLabel":613},"ch7","Ohm's law around the house","Chapter 07","7 Around the house",{"id":615,"type":43,"markdown":616},"house-intro","Every appliance on a 230 V supply gets the same push. What makes a kettle roar and a fan purr quietly is **resistance**: each appliance is designed with the resistance that lets the right current through.\n\nThat gives a surprising rule of thumb: **on the same voltage, the lower the resistance, the bigger the current, and the more powerful the appliance.** A geyser's element is low resistance on purpose. A night lamp's is high. Explore a few below and follow the chain from push to effect.",{"id":618,"type":619,"title":620,"prompt":621,"options":622},"house-explorer","explorer","Follow the chain: push, pushback, flow","Pick a device to trace how V and R set the current, and whether a 16 A breaker stays on.",[623,635,646,656,667],{"id":624,"label":625,"chain":626,"badge":631,"note":634},"torch","Torch",[627,628,629,630],"Two AA cells: 3 V","Bulb: 10 Ω","I = 3 ÷ 10","0.3 A",{"text":632,"tone":633},"Tiny current, safe to handle","yes","Low voltage and modest resistance give a small current. Even if you touched both battery ends with dry fingers, your skin's high resistance would allow only a few hundredths of a milliamp: far too little to feel.",{"id":636,"label":637,"chain":638,"badge":643,"note":645},"fan","Ceiling fan",[639,640,641,642],"Socket: 230 V","Fan motor draws ≈ 0.3 A","Acts like ≈ 770 Ω","≈ 70 W",{"text":644,"tone":633},"Well under 16 A","A motor is not a simple resistor (it pushes back more when spinning), but at full speed it draws about as much current as a 770 Ω resistance would: 230 ÷ 770 ≈ 0.3 A. That is why you can run several fans on one circuit without any trouble.",{"id":647,"label":648,"chain":649,"badge":653,"note":655},"kettle","Kettle",[639,650,651,652],"Element: ≈ 35 Ω","I = 230 ÷ 35","≈ 6.6 A",{"text":654,"tone":633},"Under 16 A","The element's low resistance is deliberate: it lets a big current through so that heat is produced fast. The kettle and a geyser together on one 16 A circuit would draw about 6.6 + 8.7 ≈ 15 A, close to the limit, which is why heavy loads get their own circuits.",{"id":657,"label":658,"chain":659,"badge":664,"note":666},"geyser","Geyser",[660,661,662,663],"Supply: 230 V","Element: ≈ 26.5 Ω","I = 230 ÷ 26.5","≈ 8.7 A",{"text":665,"tone":633},"Needs its own thick cable","One of the biggest steady currents in a typical Indian home. Thick 4 mm² wiring keeps the cable cool, and a dedicated breaker protects it.",{"id":668,"label":669,"chain":670,"badge":674,"note":677},"short","Short circuit",[660,671,672,673],"Damaged cable: ≈ 2 Ω","I = 230 ÷ 2","115 A",{"text":675,"tone":676},"MCB trips","no","With almost nothing resisting, the current shoots up to over seven times the breaker's rating. The MCB trips within a fraction of a second. Without it, the wires would overheat, melt their insulation and could start a fire.",{"id":679,"type":47,"variant":680,"title":681,"markdown":682},"house-bulb-cold","nuance","Why old bulbs pop at switch-on","A glowing 60 W bulb resists about 880 Ω (230 ÷ 880 ≈ 0.26 A). Cold, its filament resists only around a tenth to a fifteenth of that, so for the first few hundredths of a second the current is roughly ten to fifteen times bigger. That surge heats any thin, weak spot in the filament fastest, which is why filament bulbs so often blow at the moment you flick the switch.",{"id":684,"type":53,"title":685,"eyebrow":686,"navLabel":687},"ch8","What actually hurts: current through the body","Chapter 08","8 Your body",{"id":689,"type":43,"markdown":690},"body-intro","Your body is a conductor too, a salty, watery one. When it touches two points at different voltages, Ohm's law applies to it just like to a kettle element: **current through you = voltage across you ÷ your body's resistance.**\n\nAnd it is the **current** through your body, especially through the chest, that does the harm. Safety guidance gives rough bands for 50 Hz mains current:\n\n- below about **1 mA**: usually not felt;\n- **1–5 mA**: a tingle;\n- **5–10 mA**: a painful shock;\n- **10–30 mA**: muscles may clamp so you cannot let go;\n- **30–100 mA**: serious risk to breathing and heart rhythm;\n- **100 mA and above**: ventricular fibrillation, fatal if the current continues.\n\nThat is why the protective devices called **RCCBs** (or RCDs) used in modern homes are set to trip at about **30 mA** of leaking current.",{"id":692,"type":493,"title":693,"problem":694,"steps":695,"help":700},"we-skin","Same socket, dry hands versus wet hands","Suppose someone touched 230 V. Estimate the current through their body with dry skin (about 100,000 Ω) and with wet skin (about 1,000 Ω).",[696,697,698,699],"Dry skin: I = V ÷ R = 230 ÷ 100,000 = 0.0023 A = **2.3 mA**. That falls in the tingle band.","Wet skin: I = 230 ÷ 1,000 = 0.23 A = **230 mA**. That is well past 100 mA, in the band where the heart is likely to go into ventricular fibrillation, which is fatal if the current continues.","Same voltage, a hundred times less resistance, a **hundred times more current**. This is the real reason for the rule *never touch switches or plugs with wet hands*, and why bathrooms have extra safety rules.","Even the “dry” case is not safe: skin resistance drops quickly once a shock begins, and a sweaty palm or a larger contact area can bring it down a long way.",{"simplerExplanation":701},"Water on your skin makes it much easier for current to get into you. Same push, much easier path, much bigger (and deadlier) current.",{"id":703,"type":47,"variant":127,"title":704,"markdown":705},"body-careful","These numbers are illustrations, not a safety margin","Body resistance is not a fixed number. It changes with moisture, sweat, the area of contact, the path through the body, how long the contact lasts and even the voltage itself. **Mains electricity at 230 V can kill.** Never experiment with sockets, plugs, extension boards or appliance insides. Hands-on experiments in this library use batteries of 9 V or less, and anything beyond a torch-and-battery setup should be done with an adult.",{"id":707,"type":356,"prompt":708,"options":709,"explanation":720},"body-prediction","Before you open the lab: at 230 V, roughly how many times more current flows through wet skin (≈1,000 Ω) than through dry skin (≈100,000 Ω)?",[710,712,715,718],{"id":363,"label":711},"The same: voltage decides everything",{"id":713,"label":714},"twice","About twice as much",{"id":716,"label":717},"hundred","About a hundred times as much",{"id":366,"label":719},"Less: water is a good insulator","**About a hundred times as much.** The voltage is the same, and the resistance is a hundred times smaller, so I = V ÷ R is a hundred times bigger: 2.3 mA becomes 230 mA. (Pure water is actually a poor conductor, but sweat and tap water contain dissolved salts, which conduct well.)",{"id":722,"type":542,"component":723,"componentVersion":5,"config":724,"objective":739,"textAlternative":740,"help":741},"body-lab","body-current",{"voltage":155,"conditions":725},[726,729,733,736],{"id":727,"label":728,"ohms":454},"dry","Dry skin, light touch",{"id":730,"label":731,"ohms":732},"damp","Damp or sweaty hands",10000,{"id":734,"label":735,"ohms":450},"wet","Wet hands, bare feet on a wet floor",{"id":737,"label":738,"ohms":458},"gloved","Wearing a rated rubber glove","Use Ohm's law to see how the same 230 V drives wildly different currents through a body depending on its resistance.","This simplified lab fixes the voltage at 230 V and lets you choose the body's resistance. It calculates I = V ÷ R in milliamps and shows the matching effect band. Dry skin, light touch, about 100,000 Ω: 2.3 mA, felt as a tingle. Damp or sweaty hands, about 10,000 Ω: 23 mA, muscles may clamp so you might not be able to let go. Wet hands and bare feet on a wet floor, about 1,000 Ω: 230 mA, in the ventricular-fibrillation band, fatal if the current continues. A rated rubber glove, above 10¹² Ω: less than a billionth of a milliamp, not felt at all. The voltage never changes; only the resistance does, and that alone moves the outcome from a tingle to a fatal shock. The model is very simplified: real body resistance varies with path, contact area, duration and the voltage itself.",{"hints":742},[743,744],"Compare the damp and wet settings: the resistance drops ten times, so what happens to the current?","Which setting shows why electricians wear rubber gloves?",{"id":746,"type":53,"title":747,"eyebrow":748,"navLabel":749},"ch9","Four mix-ups, cleared up","Chapter 09","9 Common mix-ups",{"id":751,"type":43,"markdown":752},"mix-intro","Almost everyone starts out with a few wrong ideas about electricity, including many adults. They are not silly; they come from everyday language (“the battery ran out of current”) and from sensible-looking guesses. Here are the four big ones, and what is really going on.",{"id":754,"type":47,"variant":755,"title":756,"markdown":757},"mix-used-up","misconception","Mix-up 1: “Current gets used up by the bulb”","**The idea:** current flows out of the battery, the bulb eats some of it, and less flows back.\n\n**What really happens:** the current is the **same everywhere** in a single loop. Measure it before the bulb and after it and you get identical readings. What the bulb uses up is **energy**, not charge. Each coulomb enters the bulb with energy and leaves with less, the difference turning into light and heat.\n\n**Water picture:** a water wheel turns because water flows through it, but the same litres per second leave the wheel as enter it. The water gives up energy, not volume.",{"id":759,"type":47,"variant":755,"title":760,"markdown":761},"mix-battery-stores","Mix-up 2: “A battery is a box full of current”","**The idea:** a battery holds a stock of current (or electrons) and pours it out until it is empty.\n\n**What really happens:** a battery stores **chemical energy**. When connected into a loop, chemical reactions inside it push charge round, and the charge that leaves one end flows back into the other. A dead battery has not run out of electrons; its chemicals have run out of the reaction that provides the push, so its voltage has dropped.\n\n**Water picture:** a battery is a pump with a fuel tank, not a water tank. The water (charge) was in the pipes all along.",{"id":763,"type":47,"variant":755,"title":764,"markdown":765},"mix-voltage-danger","Mix-up 3: “Higher voltage always means more danger”","**The idea:** danger depends only on the voltage number.\n\n**What really happens:** the harm comes from the **current through your body**, and that depends on voltage **and** resistance (I = V ÷ R), plus how long it lasts and how much charge is available. Examples:\n\n- A shock from a car door or a woollen jumper on a dry day can be **several thousand volts**, yet it only stings, because the tiny amount of stored charge drains away in a split second.\n- A **12 V** car battery can drive 200 A through a starter motor, but through dry skin it pushes only about 0.12 mA, too little to feel.\n- The **same 230 V** socket gives roughly a tingle through dry skin and a likely fatal current through wet skin.\n\n**The takeaway is not “voltage is harmless”.** Higher voltage *can* drive more current through you, which is why 230 V deserves real respect and 25 kV lines can kill from a distance. It means you need to think about voltage, resistance and current together.",{"id":767,"type":47,"variant":755,"title":768,"markdown":769},"mix-thick-wire","Mix-up 4: “A thicker wire has more resistance”","**The idea:** more stuff means more obstruction.\n\n**What really happens:** a thicker wire has **less** resistance. Resistance comes from charge bumping through the material, and a thicker wire gives the charge more room: more parallel lanes to travel along. Double the cross-sectional area and the resistance halves.\n\n**Water picture:** a wide pipe carries more water for the same pump than a narrow one. That is exactly why high-current appliances like geysers are wired with *thicker* cable.",{"id":771,"type":174,"itemId":772,"prompt":773,"check":774,"hints":789,"feedback":791},"mix-practice","electricity.understand-mixup-series-current","Two identical bulbs are connected one after the other in a single loop with a battery. An ammeter between the battery and the first bulb reads 0.2 A. What does an ammeter between the two bulbs read?",{"kind":249,"options":775,"correct":788},[776,779,782,785],{"id":777,"label":778},"a","0.2 A",{"id":780,"label":781},"b","0.1 A, because the first bulb used half",{"id":783,"label":784},"c","0 A, because both bulbs share it out",{"id":786,"label":787},"d","0.4 A, because it adds up",[777],[790],"In a single loop, is there anywhere else for the charge to go?",{"correct":792,"incorrect":793},"Right: 0.2 A. In a single loop the current is the same at every point. The bulbs take energy from the charge, not the charge itself.","It is still 0.2 A. With only one path, every bit of charge that passes the first ammeter must also pass the second. Bulbs use energy, not current.",{"id":795,"type":53,"title":796,"eyebrow":797,"navLabel":798},"ch10","Looking ahead: energy and power","Chapter 10","10 What comes next",{"id":800,"type":43,"markdown":801},"power-teaser","You have now met the push, the flow and the pushback. One more pair of ideas sits right on top of them, and you have already brushed past it on the charger plate.\n\n**Power** is how fast energy is being delivered, measured in **watts (W)**. For any device:\n\n**power = voltage × current**, or **P = V × I**.\n\n- Phone charger: 5 V × 2 A = **10 W**.\n- Kettle: 230 V × 6.5 A ≈ **1,500 W** (1.5 kW).\n- Ceiling fan: 230 V × 0.3 A ≈ **70 W**, close to the 75 W on its label.\n\nIt makes sense in the water picture: a water wheel delivers more power if the water pushes harder (more voltage) *or* if more of it flows each second (more current).\n\n**Energy** is power multiplied by time. Your electricity bill counts energy in **units**, where 1 unit = 1 kilowatt-hour (kWh): 1,000 W running for one hour. A 1.5 kW kettle running for 10 minutes uses 1.5 × 10 ÷ 60 = **0.25 units**. Later layers turn this into a full bill calculator and follow those units back to the power station.",{"id":803,"type":47,"variant":680,"title":804,"markdown":805},"power-nuance","Watts are not volts are not amps","A 12 V car starter at 200 A delivers about 2,400 W, more than a kettle, from a much smaller voltage. A 230 V LED lamp might use only 9 W. Neither the voltage nor the current alone tells you how much energy something uses: you need both, multiplied together, and then the time it runs.",{"id":807,"type":808,"prompt":809},"reflection-home","reflection","Choose one appliance in your home. Find its rating plate (with an adult's help if it is heavy or fixed to a wall, and never while it is plugged in). Write down its voltage and power, then work out the current it draws with I = P ÷ V, and its resistance with R = V ÷ I. Does the answer fit where it sits on this lesson's ladders?",{"id":811,"type":811,"title":812,"questions":813},"quiz","Check yourself",[814,827,840,853,866,879,892,905,918,931],{"itemId":815,"prompt":816,"options":817,"correct":780,"why":826},"electricity.understand-quiz-voltage-meaning","Which description of voltage is best?",[818,820,822,824],{"id":777,"label":819},"The amount of charge passing a point each second",{"id":780,"label":821},"The push between two points: the energy each bit of charge gains or loses",{"id":783,"label":823},"How much a wire opposes the flow",{"id":786,"label":825},"The amount of electricity stored in a battery","Voltage is always measured between two points and tells you how much energy each coulomb of charge gains or loses between them. Option a is current; option c is resistance; a battery stores chemical energy, not voltage.",{"itemId":828,"prompt":829,"options":830,"correct":777,"why":839},"electricity.understand-quiz-voltmeter","You want to measure the voltage of a bulb in a circuit. How should the voltmeter be connected?",[831,833,835,837],{"id":777,"label":832},"Across the bulb, one probe on each side",{"id":780,"label":834},"In line with the bulb, so the current passes through the meter",{"id":783,"label":836},"With one probe touching the middle of the bulb",{"id":786,"label":838},"Anywhere, because voltage is the same everywhere","Voltage is a difference between two points, so the voltmeter goes across the part. The ammeter is the one that goes in line. Remember: voltage across, current through.",{"itemId":841,"prompt":842,"options":843,"correct":783,"why":852},"electricity.understand-quiz-drawer","A new 1.5 V AA cell sits alone in a drawer. What current flows through it?",[844,846,848,850],{"id":777,"label":845},"1.5 A",{"id":780,"label":847},"A small leak of about 1 mA",{"id":783,"label":849},"None, because there is no complete loop",{"id":786,"label":851},"It depends on how new the cell is","Current needs a complete path. The cell has a push (1.5 V) ready and waiting, but with nowhere for charge to go, no current flows. Voltage can exist without current.",{"itemId":854,"prompt":855,"options":856,"correct":780,"why":865},"electricity.understand-quiz-ohm-12-4","A 12 V supply is connected across a 4 Ω resistor. What current flows?",[857,859,861,863],{"id":777,"label":858},"0.33 A",{"id":780,"label":860},"3 A",{"id":783,"label":862},"16 A",{"id":786,"label":864},"48 A","I = V ÷ R = 12 ÷ 4 = 3 A. Option d multiplies instead of dividing (that would be V × R, which is not a meaningful quantity here).",{"itemId":867,"prompt":868,"options":869,"correct":783,"why":878},"electricity.understand-quiz-double-r","The voltage stays the same, but you swap in a part with twice the resistance. What happens to the current?",[870,872,874,876],{"id":777,"label":871},"It doubles",{"id":780,"label":873},"It stays the same",{"id":783,"label":875},"It halves",{"id":786,"label":877},"It drops to zero","I = V ÷ R. With V fixed, doubling R halves I. More pushback with the same push means less flow.",{"itemId":880,"prompt":881,"options":882,"correct":786,"why":891},"electricity.understand-quiz-wire","Which copper wire has the lowest resistance?",[883,885,887,889],{"id":777,"label":884},"Long and thin",{"id":780,"label":886},"Long and thick",{"id":783,"label":888},"Short and thin",{"id":786,"label":890},"Short and thick","Resistance rises with length and falls with thickness. A short, thick wire gives charge the least distance to travel and the most room to travel in.",{"itemId":893,"prompt":894,"options":895,"correct":780,"why":904},"electricity.understand-quiz-wet-hands","Why is touching a switch with wet hands so much more dangerous than with dry hands?",[896,898,900,902],{"id":777,"label":897},"Water raises the voltage of the switch",{"id":780,"label":899},"Wet skin has much lower resistance, so a much bigger current flows through you",{"id":783,"label":901},"Water stores electric charge and releases it all at once",{"id":786,"label":903},"It is not more dangerous; only the voltage matters","The voltage is unchanged at 230 V, but wet, salty skin can cut the body's resistance around a hundredfold. By I = V ÷ R, the current rises around a hundredfold, from a tingle to a potentially fatal level.",{"itemId":906,"prompt":907,"options":908,"correct":780,"why":917},"electricity.understand-quiz-plate","A charger plate reads OUTPUT 5 V ⎓ 2 A. Which statement is correct?",[909,911,913,915],{"id":777,"label":910},"It gives out AC at 5 V and can supply up to 10 W",{"id":780,"label":912},"It gives out DC at 5 V and can supply up to 10 W",{"id":783,"label":914},"It gives out DC and must be plugged into a 5 V socket",{"id":786,"label":916},"It always forces exactly 2 A into the phone","⎓ means DC. Power = 5 V × 2 A = 10 W at most. The phone draws what it needs up to the 2 A limit, and the input side (100–240 V ~) is what connects to the wall.",{"itemId":919,"prompt":920,"options":921,"correct":780,"why":930},"electricity.understand-quiz-conventional","In a torch circuit, which way do electrons actually drift through the wires outside the battery?",[922,924,926,928],{"id":777,"label":923},"From + to −, the same way as the arrows on circuit diagrams",{"id":780,"label":925},"From − to +, opposite to conventional current",{"id":783,"label":927},"Both ways at once",{"id":786,"label":929},"They don't move; only energy moves","Electrons are negative, so they drift from the − terminal round to the + terminal. Circuit diagrams use conventional current (+ to −), a choice made long before electrons were discovered.",{"itemId":932,"prompt":933,"options":934,"correct":783,"why":943},"electricity.understand-quiz-mcb","A 16 A breaker protects a 230 V circuit. Which of these would make it trip?",[935,937,939,941],{"id":777,"label":936},"A 35 Ω kettle element",{"id":780,"label":938},"An 880 Ω bulb",{"id":783,"label":940},"A fault leaving 5 Ω between live and neutral",{"id":786,"label":942},"A phone charger drawing 0.05 A","230 ÷ 5 = 46 A, far above 16 A, so the breaker trips. The kettle draws about 6.6 A and the bulb about 0.26 A, both safely under the limit.",{"id":945,"type":946,"title":947,"points":948},"cheat-sheet","summary","Cheat sheet",[949,950,951,952,953,954,955,956,957,958,959,960,961,962,963],"**Water picture:** battery = pump, charge = water already in the pipes, current = flow rate, resistance = a narrow pipe.","**Voltage (V, volts):** the push, always *between two points*. 1 V = 1 joule per coulomb. Measured with a voltmeter **across** a part.","**Everyday voltages:** AA 1.5 V · USB 5 V · car 12 V · Indian socket 230 V (USA 120 V) · railway 25 kV · transmission 400 kV · lightning ≈ 100 million V+.","**Current (I, amps):** the flow, charge per second. 1 A ≈ 6.24 × 10¹⁸ electrons per second. Measured with an ammeter **in line**.","**Everyday currents:** LED 20 mA · fan ≈ 0.3 A · kettle ≈ 6.5 A · geyser ≈ 9 A · car starter ≈ 200 A · lightning ≈ 30,000 A.","**Conventional current** runs + → −; electrons actually drift − → +.","**Resistance (R, ohms Ω):** the pushback. Higher for longer wires, thinner wires, poorer conductors and (in metals) hotter wires.","**Resistance is useful** in heaters, kettles, geysers and bulbs; wasteful in connecting wires.","**Ohm's law:** V = I × R, I = V ÷ R, R = V ÷ I. Double V → double I; double R → half I.","**Voltage without current** is common (a battery in a drawer). Current needs a complete loop.","**Current is not used up.** It is the same all round a single loop; energy is what gets used.","**Batteries store chemical energy,** not current.","**Harm comes from current through the body.** 230 V through wet skin (≈1,000 Ω) ≈ 230 mA: ventricular fibrillation, fatal if it continues. Never touch mains with wet hands.","**MCBs and fuses** watch current: a short circuit (tiny R) makes a huge current and trips them.","**Coming next:** power P = V × I (watts); energy = power × time; 1 unit = 1 kWh.",{"id":965,"type":965,"sourceIds":966},"sources",[967,968,969,970,971,972,973,974],"elec-understand-physicsclassroom-ohms-law","elec-understand-hyperphysics-current","elec-understand-hyperphysics-resistance","elec-understand-hyperphysics-ohms-law","elec-understand-nist-ampere","elec-understand-hyperphysics-shock","elec-understand-nws-lightning-power","elec-understand-nssl-lightning-faq",[967,968,969,970,971,972,973,974],"needs_review",{"generatedBy":978,"notes":979},"claude-code","Draft generated locally; pending owner review.","d9bc43b2e95dfed8b563a2af64ab0c993b879a965a7478194d4e5d863325a853",{"diagram:water-circuit":982,"logic:practice":983,"component:ohms-law@1":984,"component:body-current@1":985,"source:elec-understand-hyperphysics-current":986,"source:elec-understand-hyperphysics-ohms-law":987,"source:elec-understand-hyperphysics-resistance":988,"source:elec-understand-hyperphysics-shock":989,"source:elec-understand-nist-ampere":990,"source:elec-understand-nssl-lightning-faq":991,"source:elec-understand-nws-lightning-power":992,"source:elec-understand-physicsclassroom-ohms-law":993},"d48e7640f9ecfa326ceaad02b29b3caa4a5224b398dda8e58b34aa4567005067","3d6b0fe1b15255975a32b0fcd94e8019bc959ad45cbf12e136e86149549c6878","8e5bbfb66fe919a96db1fce1b9d535d2b3c030c57cf90efb2c7172829a413105","f0549ba48695a6eaaed9595ef662beb1f8ecdf653291224c59ff4fd1a0fe101a","8c64850ff865ae262b81c10f265097eb947f08ba795ff3838384ed80689e59e7","2f1580271ae5c3c66a0b9d91880f272ac1a208912a370f94b4453e693bceb39d","981387e523c7899ab00b6ab020c8cad8693baf0b8f58b826915daffc92025626","8a8b3b598067a6be6d60b25fa0daa68cf1a0707d4fd5945c7b80a84da56380c4","32506a99535aaeef46f6f86c5419d376774279fa381bea48088a5056151ff3a2","57f583af80f06a5f965794d41ff475c6cf99f760df8ff42f6a133719b0983b61","480d61614057177209f64dd02fd0e7262556431107deb69d9bf1d3be9450b484","66a0c26c9974ab9ed963d1520e2458669bae40b243ea51066e3f2676f12fde27",{"state":995,"reviewer":996,"selfReview":997,"reviewedAt":998,"method":999},"approved","The library owner",true,"2026-09-20T10:18:37.581Z","owner_bulk","preview-7e1cbbcc4f",1789899599710]