Know that the p.d. between two points is measured in volts (V)

4.2.3 Electromotive Force and Potential Difference

What is Potential Difference?

⚡️ The potential difference (p.d.) between two points in an electric circuit is the amount of energy per unit charge that moves from one point to the other. It is measured in volts (V), just like we measure height in metres or weight in kilograms. Think of it like the difference in water height between two points in a pipe – the higher the water level, the more “push” it has to flow downwards. In a circuit, a higher p.d. means a stronger “push” for electrons to flow.

Electromotive Force (EMF)

🔋 EMF is the energy supplied by a source (like a battery) that drives electrons through a circuit. It is the maximum potential difference the source can provide when no current is flowing. In a simple battery, the EMF is the voltage you read on a voltmeter when the battery is not connected to a load.

Key Relationships

• Potential difference between two points: $V = \frac{W}{Q}$, where $W$ is work done and $Q$ is charge.
• EMF of a battery: $E = V_{\text{open-circuit}}$.
• When a load is connected, the actual p.d. across the load is less than the EMF due to internal resistance.

Exam Tip Box

📌 Remember: The symbol for potential difference is $V$, and its unit is the volt (V). When you see a question about “voltage across a resistor”, they are asking for the p.d. between its two ends. Always check whether the circuit is open (no current) or closed (current flowing) – this tells you whether you should use EMF or actual p.d.

Practical Example

Imagine a battery with EMF $E = 1.5\,\text{V}$ and internal resistance $r = 0.2\,\Omega$. If a resistor $R = 5\,\Omega$ is connected, the current $I$ is: $$I = \frac{E}{R + r} = \frac{1.5}{5 + 0.2} \approx 0.29\,\text{A}$$ The p.d. across the resistor is: $$V_R = I \times R \approx 0.29 \times 5 = 1.45\,\text{V}$$ Notice $V_R$ is slightly less than the EMF because of the voltage drop across the internal resistance.

Quick Reference Table

Exam Tip Box – Calculations

📐 When you calculate the p.d. across a component:

1. Find the total resistance $R_{\text{total}} = R_{\text{load}} + r_{\text{internal}}$.
2. Use Ohm’s law to find current $I = \frac{E}{R_{\text{total}}}$.
3. Multiply current by the load resistance to get $V_{\text{load}} = I \times R_{\text{load}}$.