# Lesson 5: Voltage and Current

## Introduction

In this lesson we'll try and get a handle on what voltage and current mean. We'll see how we can measure them and we'll also look at some simple calculations of voltage and current. Finally we'll look at Kirchoff's Current Law and Kirchoff's Voltage Law.

## What the words mean: voltage, potential and potential difference

The idea of electrical potential energy (or potential for short) is quite strictly defined but for most of the time we can say that voltage and potential mean the same thing. Potential difference, or p.d. is just the same as voltage difference. So when you hear the word 'potential' to do with electricity you're pretty safe just thinking 'voltage'.

## The simple meaning of voltage

A common way of thinking about voltage is that it's the 'push' from a battery. We're not going to take this approach, however. We're going to define voltage in terms of energy.

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Remember our animation that helps us keep track of charges and energy around a circuit. Again we're not pretending that this is what really happens.

One thing you'll notice is that the amount of energy (red stuff) that each charge has changes around the circuit. You can think of voltage as the amount of energy that a charge has at any point in the circuit.

So we can say that the voltage is high on one side of the circuit, zero on the other side of the circuit and decreases as you go from one side of a bulb to the other.

So when you think of voltage think energy. And when you think of energy think red stuff.

## The simple meaning of current

Again, looking at our animation you can see that the charges (black blobs) move around the circuit.

So a very basic notion about current is that it is a flow of charges. The size of the current has something to do with the speed the charges are moving. The faster they move the bigger the current.

The charges don't have to be electrons. They can be ions like when salty water conducts or a mixture of ions and electrons like in lightning and sparks.

So for current think moving charges. And when you think about moving charges think black blobs.

## Using a voltmeter to measure voltage

The unit of voltage is the volt. We'll see how we define the volt in a second but first let's learn how to use a voltmeter.

Voltmeters measure voltage *difference*. This is sometimes called potential difference (p.d.). They mean exactly the same thing.

Using a voltmeter you compare the amount of energy (red stuff) that charges have at one point in the circuit with the amount they have at another.

What this means is a voltmeter measures the *difference* in voltage between two points. So you always have to connect both leads of a voltmeter. Voltage has nothing to do with flow. That's why we always talk about the voltage 'across' a component or 'between' two points. We never talk about a voltage 'through' something.

If you connect the two leads to the voltmeter first you can then use them to sample the voltage between any two points, for example across a bulb or across the terminals of a battery. We say that the voltmeter is always connected in parallel with the thing you're measuring the voltage across. ?>

If you connect a voltmeter in series, by breaking the circuit and inserting the voltmeter, then it won't work in the way you might expect.

Most leads that you see at school are covered in plastic insulation so you can only make a connection at the ends.

But you can see from our animation that it's perfectly sensible to talk about the potential difference between any two points, even if you can't insert a voltmeter there in real life. For example the difference between any point where the charges have all their energy and any point where they have none is bound to be 6 volts.

## Potential difference tells you where energy is converted

Energy is converted where there is a potential difference. The p.d. across a lit bulb will be, say, 6 volts, depending on what kind of circuit it's connected in.

By saying the p.d. across a bulb is 6 volts you're saying 'as a charge moves from one side of the bulb filament to the other it loses one joule of energy per coulomb of charge.'

You can also measure the p.d. across the ends of a wire. If the whole length of the wire is at 6 volts then the p.d. across its ends will be 0 volts. This makes sense because no energy is converted in the wire.

By saying the p.d. across the ends of a wire is 0 volts you're saying 'as a charge moves from one end of the wire to the other it won't lose any energy.'

## Using an ammeter to measure current

You can think of an ammeter as a bit like a speedometer for charges.

In order to measure the speed of the charges we need the charges to go through the ammeter. This means breaking the circuit and putting the ammeter in the way. This is called connecting the ammeter in series.

If you connect the ammeter in parallel then it won't work in the way you might expect.

The animation shows that the charges are moving at the same speed everywhere. In other words the current is the same everywhere. So it doesn't matter where you insert the ammeter in a simple series circuit it will always measure the current correctly.

## The coulomb as the unit of charge

Our animations show little black blobs and we've said that these are 'charges'. What we really mean is that they're little particles, like electrons or ions, that carry this property called electric charge. You can't really define what electric charge is. It's just a fundamental property of matter, like mass.

When you talk about a distance you don't know you might call it d, for distance. You might call a time, t or a mass, m. You tend to call charge, Q, which may seem a bit odd, but it's because it originally stood for 'Quantity' of charge.

The amount of electric charge an object has is measured in a unit called the coulomb. It's named after the French scientist Charles-Augustin de Coulomb, who was an aristocrat living at the end of the 1700s, when the French Revolution was in full swing.

The charge on a single electron is about 0.00000000000000000016 coulombs. The abbreviation is written with a capital C because it's named after a person but the word is written with a small c.

So when you ask how much charge has this balloon gained when I rubbed it on my woollen jumper the answer might be something like 'a few trillionths of a coulomb'. In electric circuits the amount of charge we deal with is much bigger and we often have many coulombs of charge flowing at the same time. ?>

A wire less than one millimeter long still has more than a coulomb of free electrons. But we don't really ever notice the huge forces that there would be if the electrons were isolated because the net charge is balanced by the positive ions.

## Simple calculations of voltage

Voltage tells us the number of joules of energy for each coulomb of charge. 1 volt means 1 joule of energy for each coulomb of charge. 2 volts means 2 joules per coulomb and so on.

So we can use the formula: voltage = energy / charge

The unit of voltage (or potential difference) is the volt, named after the 18th Century Italian inventor of the battery, Count Alessandro Volta. The abbreviation of the unit is V.

It can be a bit confusing because V is normally used for the quantity, voltage as well as the unit of voltage, the volt. So you may see something like

V = 2.5 V

This means 'the voltage is 2.5 volts'.

If 6 C of charge transfer 12 J of energy as they pass through a bulb then the p.d. across the bulb must be 2 V, because each coulomb of charge has transferred 2 J of energy.

You may have come across the formula voltage = current x resistance, which is sometimes called Ohm's law. This doesn't really define the volt, even though the formula has voltage in it.

The strict definition of the volt actually relates power and current rather than energy and charge.

## Simple calculations of current

We've said that the size of electric current is something to do with the speed that the charges are moving at. In fact what we want to know is how many coulombs of charge pass a point in a circuit each second.

So an ammeter acts a bit like a charge counter that resets every second.

The common abbreviation for current is I. This is because current used to be thought of in terms of its 'intensity'.

The unit of current is the ampere, named after another 18th century French scientist, Andre-Marie Ampere. The unit is often abbreviated to the amp or just A.

1 ampere means 1 coulomb of charge passes a point each second. 2 amperes means 2 coulombs of charge pass a point each second and so on. Even though it would seem that an ampere should be defined as 1 coulomb passing a point each second this is not the strict definition.

## Speed of charges in different thickness of wire

In our animations we show the same thickness of wire all the way round a circuit and this wire only allows single black blobs to pass. So for a constant current we always show the charges moving at the same speed one blob thick.

In a real circuit there are connections and different thicknesses of wire. So in a real series circuit the current is still exactly the same all the way around but the speed of the charges isn't.

What happens to the speed of the charges to keep the current the same?

When the charges go from a thick wire to a thin wire then fewer of them can go through side-by-side and so they have to go quicker. When they go from a thin wire to a thick wire more of them can go through side-by-side and they slow down.

This is the opposite of what you might expect.

## Kirchoff's Laws

There are two very simple laws about current and voltage by the German physicist Gustav Kirchoff in 1845 while he was a 23 year-old student.

Kirchoff's 1st Law says that the current flowing into a junction is always the same as the current flowing out.

Kirchoff's 2nd Law essentially says that if you add up the voltages across all the components in a circuit the result must be the same as the battery voltage.