Electricity

Why This Matters

Flick a switch and a room lights up. Plug in a charger and your phone slowly fills up again. Look around you. Fans, fridges, phones, trains — almost everything runs on the same invisible thing flowing through wires. But what is really flowing inside those wires? And here is a puzzle: a heater coil glows red-hot, but the wire bringing power to it stays cool. Why?

This chapter answers all of that. You will learn what electric current really is. You will learn what pushes it along (voltage). You will learn what slows it down (resistance). And you will learn one simple rule, called Ohm’s law, that links all three together. Once you know this rule, you can work out what any simple circuit will do.

This is not just theory. Why does a fuse “blow”? Why are the appliances in your house wired in parallel and not in series? Why is your electricity bill measured in “units”? By the end of this chapter, all of these will make complete sense.

The Big Idea

Current is the flow of electric charge. A potential difference (also called voltage) is the push that drives that charge through a wire. Resistance is whatever slows the charge down. Ohm’s law links all three: V = IR. Push harder (more V) and you get more current. Slow it down more (more R) and you get less current.

The easiest way to picture this is water flowing in a pipe. The voltage is like the water pressure that makes the water flow. The current is how much water flows past a point each second. The resistance is how narrow or blocked the pipe is. A narrow, clogged pipe lets less water through. That is the whole chapter in one picture. The rest is just this idea made exact, and then used for groups of resistors, heating, and power.

Let’s Break It Down

Electric current

Before we talk about current, let’s quickly refresh what charge and electrons actually are — because that is the stuff doing the flowing.

First, what is charge? Charge is a basic property of tiny particles. Electrons carry charge, and that is what moves through wires. When this electric charge flows through a conductor (a material that lets charge pass through it easily, like a metal wire), we say there is an electric current in it. So current means charge is flowing.

Current is the rate of flow of charge. In simple words, it tells you how much charge passes a point in the wire each second. More charge per second means more current.

Suppose a charge Q flows past one spot in the wire in a time t. Then the current I is:

I = Q / t

Now the units. The SI unit of charge is the coulomb (C). One coulomb is the charge of about 6 × 10¹⁸ electrons. (Each single electron carries a very tiny charge of 1.6 × 10⁻¹⁹ C, so you need a huge number of them to make one coulomb.) The SI unit of current is the ampere (A). One ampere means one coulomb of charge flows past a point every second (1 A = 1 C/s). Currents in small devices are often much smaller, so we use milliamperes (1 mA = 10⁻³ A, one-thousandth of an ampere) or microamperes (1 µA = 10⁻⁶ A, one-millionth of an ampere).

To measure current we use an ammeter. An ammeter is always connected in series in the circuit. “In series” means it is placed in the same line as the wire, so all the current passes straight through it.

Here is one thing that surprises many students. Inside a metal wire, the particles that actually move are the electrons, and electrons carry negative charge. But when scientists first studied current, electrons had not been discovered yet. So they fixed a rule: the direction of current is the direction in which positive charge would move. This means the current direction is taken as opposite to the way the electrons really flow. So we say current flows from the + terminal of the cell, through the circuit, to the − terminal.

Let’s put I = Q/t to work. Here’s a quick one: if we know the current and how long it flows, can we find the total charge?

Potential difference (voltage)

Charge will not flow on its own. Think of water in a pipe lying flat on the ground. The water just sits there, because there is nothing to push it. To make charge flow, you need a “push.” This push is a difference in electric pressure between two points, and we call it the potential difference (or voltage). A cell or a battery creates this push using chemical energy. The push is there even before any current starts to flow.

We keep mentioning the cell and the circuit, so let’s pin down exactly what each one is before going further.

So what exactly is potential difference? The potential difference V between two points is the work done (W) to move one unit of charge (Q) from one point to the other. Work just means the energy spent to move the charge. In short, voltage tells you how much energy each bit of charge carries.

V = W / Q

The SI unit is the volt (V). One volt is the potential difference when 1 joule of work is needed to move 1 coulomb of charge:

1 V = 1 J/C

To measure potential difference we use a voltmeter. A voltmeter is always connected in parallel. “In parallel” means it is connected across the two points whose voltage you want to measure, on a side branch, not in the main line.

Let’s see V = W/Q in action — this time finding the energy (work) needed to push a charge across a known voltage.

Circuit diagrams

Drawing every battery and bulb as a real picture takes too long. So instead we use simple standard symbols that everyone agrees on. A closed, unbroken path for the current to flow around is called an electric circuit. If you break this path anywhere, the current stops at once. This is exactly what a switch does.

Figure 11.1 below shows what a real circuit looks like once we replace the picture of every part with its symbol.

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Here are the most common symbols. A cell is shown as one long line (the + terminal) and one short line (the − terminal). A battery is just several cells joined together. A switch (also called a plug key) can be drawn open or closed. A resistor is drawn as a zig-zag or a rectangle. A rheostat is a resistor whose value you can change. An ammeter is a circle with the letter A inside it, and a voltmeter is a circle with the letter V inside it.

Ohm’s law

This is the most important rule in the chapter. In 1827, a scientist named Georg Simon Ohm did experiments on metal wires. He found that the potential difference V across a metal conductor is directly proportional to the current I flowing through it. “Directly proportional” means that if you double V, then I also doubles. This is true as long as the temperature of the wire stays the same.

V ∝ I, so V = IR

The constant R in this equation is the resistance of the conductor. Resistance is how strongly the conductor opposes the flow of charge. A high resistance fights the current hard. Its SI unit is the ohm, written with the symbol Ω.

We can rearrange V = IR in two useful ways:

R = V / I and I = V / R

If 1 volt pushes a current of 1 ampere through something, then its resistance is 1 Ω. Look carefully at the last form, I = V / R. For a fixed voltage, more resistance means less current. For example, if you double the resistance, the current drops to half. A device that you can adjust to change the resistance, and so control the current, is called a rheostat.

If you draw a graph of V (on the up-and-down y-axis) against I (on the across x-axis) for such a conductor, you get a straight line passing through the origin (the point 0,0). That straight line is Ohm’s law shown as a picture. The steepness (slope) of the line is equal to the resistance R. Figure 11.2 below shows this graph.

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Time to use I = V/R. Let’s see how the same 220 V supply gives very different currents to a high-resistance bulb and a low-resistance heater.

What resistance depends on

So what makes one wire resist current more than another? To answer that, we first need to know where resistance even comes from. Picture the inside of the wire: the metal atoms sit fixed in place, and the free electrons drift through the gaps between them. Figure 11.3 below zooms inside the wire to show this.

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So resistance is really just electrons bumping into atoms. Every bump slows an electron down and steals a little of its energy. Now the three factors make perfect sense:

• It is directly proportional to the length (l). A longer wire has more resistance. (Charge has to push through more wire.)
• It is inversely proportional to the area of cross-section (A). The cross-section is how thick the wire is when you cut across it. A thicker wire has less resistance. (Charge has more room to flow.)
• It depends on the material the wire is made of. Copper and rubber behave very differently.

We can put all three together in one formula:

R = ρ × (l / A)

Here ρ (the Greek letter rho) is the resistivity of the material. Resistivity is a number that belongs to the material itself, no matter what shape it is in. It tells you how good or bad that material is at carrying current. It is measured in Ω m (ohm metre). Good conductors like silver and copper have very low resistivity (about 10⁻⁸ Ω m), so current flows easily. Insulators like glass and rubber have huge resistivity (10¹² Ω m or even more), so current can barely get through. That is exactly why wires are made of copper and their covering is made of rubber.

Figure 11.4 below sums up all three factors side by side, so you can see at a glance how length, thickness and material each pull resistance up or down.

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Here are a few useful facts. An alloy is a mixture of metals. Alloys like nichrome have higher resistivity than pure metals. They also do not get spoiled (oxidise) easily when they get hot. Both of these make alloys perfect for the heating parts inside toasters and irons. Tungsten is used for the thin wire (filament) inside bulbs because it has a very high melting point, so it can glow white-hot without melting. Copper and aluminium are used in the long power lines that carry electricity to your home, because their low resistivity wastes very little energy on the way.

Let’s test how well you can read R = ρl/A: what happens to the resistance if we halve the length and double the thickness of the same wire?

Resistors in series

When resistors are joined end to end, one after another in a single line, we say they are in series. In a series connection, the same current flows through every resistor (there is only one path, so the current has nowhere else to go). The voltages across the separate resistors add up to give the total voltage. The combined resistance (called the equivalent resistance) is simply the sum of all of them:

But why is the current the same everywhere while the voltage gets shared out? Think of the water-pipe picture again. Figure 11.5 below imagines one single loop of pipe with a pump and two waterwheels, one after the other, with no branches anywhere.

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Here is the key. Because there is only one pipe and no junction, every drop of water that leaves the pump must pass through both wheels and come back. Nothing can pile up or escape on the way. So the amount of water flowing past every point each second is the same — that is why the current is identical through each resistor. The push (voltage) is different, though. Each wheel “uses up” some of the pump’s pressure to turn. So the pump’s total push is shared between the wheels, which is why the voltages add up: V = V₁ + V₂.

The same idea as a real circuit diagram is shown in Figure 11.6 below.

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Rₛ = R₁ + R₂ + R₃

The total resistance in series is always larger than any single resistor in the line. There is one big drawback. Since there is only one path, if even one part fails, the whole circuit breaks and everything stops. You may have seen this with old string lights for Diwali: if one bulb fuses, the whole string goes dark.

Let’s put the series rules together in one go — finding the total resistance, the single current, and how the voltage splits between two parts.

Resistors in parallel

When resistors are joined side by side between the same two points, we say they are in parallel. Now each resistor is its own separate branch. The voltage across each branch is the same, because they all connect to the same two points. The current splits up among the branches, and the separate currents add up to the total. The equivalent resistance is found using a “reciprocal” rule, which means we add up 1 divided by each resistance:

This is the opposite of series, so let’s see why with the same water picture. In Figure 11.7 below the pipe splits at a junction into two separate branches, each with its own wheel, and the branches join up again.

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Here is the reason. Both branches begin at the same point X and end at the same point Y. The difference in “pressure” between X and Y is a single, fixed amount. So every branch stretched between X and Y feels exactly that same push — that is why the voltage is the same across each branch. But the water now has a choice of paths, so it splits up between them. The flows in the branches then add back together, which is why the currents add: I = I₁ + I₂.

The same idea as a real circuit diagram is shown in Figure 11.8 below.

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1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃

The total resistance in parallel is always smaller than the smallest single resistor. This sounds strange at first, so Figure 11.9 below pictures a crowd of people trying to get through a wall with just one doorway versus the same wall with two doorways.

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The reason it feels strange is that in everyday life “adding more” usually means “more total.” But adding a parallel branch is like opening another door: it never closes the door you already had. It only gives the current an extra way through. With more ways through, the same push moves more current, and “more current for the same push” is exactly what lower resistance means. That is also why we add the 1/R values, not the R values — each branch adds to how easily current flows, and easiness is 1/R. This is exactly why the appliances in your home are wired in parallel. Each one gets the full 220 V it needs. Each can be switched on or off on its own. And if one stops working, the rest keep running.

Now let’s work a full parallel example: three different resistors across one battery, finding each branch current and proving the total resistance really does come out smaller than the smallest branch.

Heating effect and electric power

To keep the current flowing, the source (cell or battery) has to keep spending energy. In a circuit that has only resistance, all of this energy turns into heat. This is called the heating effect of current. The amount of heat produced is given by:

H = VIt = I²Rt

This is known as Joule’s law of heating. It tells us that the heat depends on three things: the square of the current (I²), the resistance (R), and the time (t). The “square of the current” part is important. It means that even a small rise in current produces a lot more heat.

But why does pushing current through a wire make it hot at all — and why does double the current give so much more heat? It comes straight from those electron-atom bumps we just met. Figure 11.10 below shows what is happening.

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So the heat is simply all those collisions adding up. Each bump turns a little of the electron’s push-energy into the jiggling of the atoms, and jiggling atoms is heat. Now, why I² and not just I? Doubling the current means roughly twice as many electrons, each also moving faster. So you get more bumps and harder bumps — the two effects multiply together, and the heat shoots up about four times. This heating effect is what makes heaters, irons, toasters and bulbs work. It is also the idea behind the fuse. A fuse is a thin piece of wire that melts and breaks the circuit if the current becomes too large and dangerous, protecting your devices.

We often want to know how fast energy is being used, not just the total. The rate at which energy is used is called electric power:

P = VI = I²R = V²/R

The SI unit of power is the watt (W). One watt means one joule of energy used per second (1 W = 1 V × 1 A). To get the total energy, use Energy = power × time. For your electricity bill, joules are too small to be handy, so power companies use a bigger unit called the kilowatt-hour (kW h). This is the “unit” you see on the bill:

1 kW h = 3.6 × 10⁶ J

So how does all this turn into the rupees on your electricity bill? Let’s actually cost out a fridge running every day for a month.

Common Mistakes

Quick Check

Practice Problems

Summary

• Current I = Q/t is how fast charge flows. Its SI unit is the ampere (A). Current flows opposite to the electrons. It is measured by an ammeter, connected in series.
• Potential difference V = W/Q is the push that drives the current. Its SI unit is the volt (V) (1 V = 1 J/C). It is measured by a voltmeter, connected in parallel.
• Ohm’s law: V = IR. Resistance R (in ohms, Ω) opposes the current. The V–I graph is a straight line through the origin.
• Resistance R = ρl/A. It is directly proportional to length, inversely proportional to area, and depends on the material through its resistivity ρ.
• Series: same current through all; Rₛ = R₁ + R₂ + R₃ (bigger than any one). Parallel: same voltage across all; 1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃ (smaller than the smallest).
• Heating effect: H = I²Rt (Joule’s law). Used in heaters and bulbs, and in the safety fuse.
• Electric power: P = VI = I²R = V²/R, measured in watts. Energy is sold in kilowatt-hours (1 kW h = 3.6 × 10⁶ J).

What’s Next

You now know how current flows, and how resistance and voltage control it. But electricity has one more amazing trick. A wire that carries current makes a magnetic field around it. And the opposite is also true: a moving magnet can create a current in a wire. This two-way link between electricity and magnetism is what makes every electric motor spin. It is also how almost all the electricity you use is generated.

In Chapter 12: Magnetic Effects of Electric Current, you will learn about magnetic field lines, the field around a wire and around a coil, how a motor spins, how a moving magnet makes current (electromagnetic induction), and how a generator turns motion into electricity.