Potential difference

What pushes the charge?

Water in a tank flows through a pipe when one end is at a higher level than the other. A ball rolls down a slope. Something must push the charge in a wire too. This is the potential difference.

Think of a pump that lifts water to a higher tank. The water then flows down through a pipe. The pump gives the water its energy. In an electric circuit, the cell is the pump. It uses the energy of a chemical reaction to push the charge, so the charge flows in the wire.

Potential difference

The potential difference between two points of a circuit is the work done to carry a unit of charge from one point to the other:

Here $W$ is the work done (the energy) in joule, and $Q$ is the charge in coulomb. The unit of potential difference is the volt (V):

So one volt is the potential difference between two points when $1\ \text{J}$ of work is done to move $1\ \text{C}$ of charge between them.

If we want the work, $W = V \times Q$. For a charge $Q$ that goes through a potential difference $V$, this is the energy that the charge takes in (in a cell) or gives out (in a bulb).

You should find that doubling the charge doubles the energy, and so does doubling the voltage.

Cells and batteries

A cell is a source of potential difference. The chemical reaction in it keeps a potential difference between its two terminals, so the cell can push the charge round the circuit as long as the reaction goes on.

• A common dry cell gives $1.5\ \text{V}$.
• A battery is a number of cells joined together. Four cells of $1.5\ \text{V}$ in series give $6\ \text{V}$.
• A car battery gives $12\ \text{V}$, and the mains supply of a house gives $220\ \text{V}$ in many countries.

Measuring potential difference: the voltmeter

A voltmeter measures the potential difference between two points. We connect it in parallel with the part of the circuit that we want to measure, so that its two ends are on the two points. A voltmeter has a very large resistance, so almost no current goes into it, and it does not change the circuit. The positive terminal of the voltmeter is joined to the point that is nearer to the positive terminal of the cell.

Look again at the circuit in the last lesson. The ammeter is in series, and the voltmeter is in parallel with the bulb.

A worked example

How much work is done to move a charge of $4\ \text{C}$ through a potential difference of $3\ \text{V}$?

We want $W$, so $W = V \times Q = 3\ \text{V} \times 4\ \text{C} = 12\ \text{J}$.

Another example

The work done to carry $4\ \text{C}$ from one point to another is $28\ \text{J}$. What is the potential difference?

$V = \dfrac{W}{Q} = \dfrac{28\ \text{J}}{4\ \text{C}} = 7\ \text{V}$.

Practise with new numbers

Try it in Python

The program finds the energy that four sources give to a charge of $2\ \text{C}$.

Remember these

• A potential difference pushes the charge round a circuit. A cell keeps a potential difference between its terminals.
• $V = \dfrac{W}{Q}$. The unit is the volt: $1\ \text{V} = 1\ \text{J/C}$.
• A voltmeter is connected in parallel. An ammeter is connected in series.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. How much energy does a charge of $5\ \text{C}$ take from a $1.5\ \text{V}$ cell?

2. What does $1\ \text{V}$ mean?

3. A battery is four $1.5\ \text{V}$ cells in series. What is its voltage, and how much energy does each coulomb take from it?

4. How much work moves $2.5\ \text{C}$ through a potential difference of $9\ \text{V}$?