The big three: voltage, current, resistance

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.

Those 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.

In 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.

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.

Imagine 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.

Now swap the words:

• The pump is the battery or the socket. It provides the push. That push is voltage.
• The water is electric charge, mostly electrons that were already sitting in the metal before you switched anything on.
• How much water passes a point each second is the flow. That flow is current.
• 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.
• The wide, smooth pipes are the connecting wires, which let charge through with very little fight.

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.

Notice 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.

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.

The 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:

• An AA cell marked 1.5 V gives every coulomb of charge that passes through it 1.5 joules of energy.
• A 230 V socket gives every coulomb 230 joules, over 150 times as much.

That is why a socket can boil water and an AA cell cannot: each packet of charge arrives carrying far more energy.

That last card is the one most people miss. Voltage is always between two points.

When 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.

This 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.

A few things jump out from that ladder.

• 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.
• 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.
• 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.
• 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.
• Lightning has no neat single value. Estimates range from about 100 million to a billion volts between cloud and ground.

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.

Here is what a typical phone charger says (the wording varies slightly between brands):

Two quick things you can already work out from the plate.

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.

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.

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.

The 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:

1 A ≈ 6,240,000,000,000,000,000 electrons passing every second.

Six 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.

Smaller currents are measured in milliamps (mA): 1 mA is one thousandth of an amp, so 1,000 mA = 1 A.

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.

Big 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.

Here is a puzzle. A fresh AA cell sitting in a kitchen drawer is 1.5 V. How much current is flowing through it?

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.

This 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.

Resistance is how strongly something opposes the flow of current. In the water picture it is a narrow, rough or clogged section of pipe.

Inside 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.

The 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.

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.

Look 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.

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.

• 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.
• 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.
• In electronics, small parts called resistors are added on purpose to limit current, for example to stop an LED from burning out.

When you look at an appliance, ask: where is the resistance, and is it the useful part or the wasteful part?

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:

voltage = current × resistance, or V = I × R.

Read 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:

• Push harder (more V) through the same resistance and more current flows. Double V, double I.
• Resist more (more R) with the same push and less current flows. Double R, half I.

That is everything Ohm's law says. The three versions below are the same rule rearranged, so you can find whichever quantity is missing.

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.

A 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.

The MCB does not care about voltage directly. It watches current, because current is what heats wires.

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.

That 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.

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.

And 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:

• below about 1 mA: usually not felt;
• 1–5 mA: a tingle;
• 5–10 mA: a painful shock;
• 10–30 mA: muscles may clamp so you cannot let go;
• 30–100 mA: serious risk to breathing and heart rhythm;
• 100 mA and above: ventricular fibrillation, fatal if the current continues.

That is why the protective devices called RCCBs (or RCDs) used in modern homes are set to trip at about 30 mA of leaking current.

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.

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.

Power is how fast energy is being delivered, measured in watts (W). For any device:

power = voltage × current, or P = V × I.

• Phone charger: 5 V × 2 A = 10 W.
• Kettle: 230 V × 6.5 A ≈ 1,500 W (1.5 kW).
• Ceiling fan: 230 V × 0.3 A ≈ 70 W, close to the 75 W on its label.

It 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).

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.