Define potential difference (p.d.) as the work done by a unit charge passing through a component

4.2.3 Electromotive Force and Potential Difference

What is Potential Difference?

Potential difference (p.d.) is the amount of work done by an external source to move a unit charge from one point to another in an electric circuit. Mathematically, it is expressed as: $$V = \frac{W}{q}$$ where V is the potential difference in volts (V), W is the work done in joules (J), and q is the charge in coulombs (C). Because we use a unit charge (1 C), the formula simplifies to: $$V = W$$ so the potential difference is numerically equal to the work done per coulomb.

Analogy: Water Flow

Think of an electric circuit like a water pipe. - The pressure difference between two points in the pipe pushes water through. - In an electric circuit, the potential difference (voltage) pushes electrons through the wires. Just as a higher pressure difference means more water can flow, a higher potential difference means more current can flow through a component.

Examples of Potential Difference in Everyday Devices

• 🔋 Battery: A typical AA battery provides about 1.5 V.
• 💡 Light bulb: A 60 W bulb in a 120 V mains supply has a potential difference of 120 V across it.
• 📱 Mobile phone charger: Supplies 5 V to charge the battery.

Calculating Work Done by a Unit Charge

If a charge of 2 C moves through a component with a potential difference of 3 V, the work done is: $$W = V \times q = 3\,\text{V} \times 2\,\text{C} = 6\,\text{J}$$ Since we are interested in the work per unit charge, we divide by the charge: $$V = \frac{W}{q} = \frac{6\,\text{J}}{2\,\text{C}} = 3\,\text{V}$$ This confirms that the potential difference is 3 V.

Table: Common Components and Their Typical Potential Differences

Key Takeaways

1. The potential difference is the work done per unit charge.
2. It is measured in volts (V).
3. Higher p.d. pushes more current through a component.
4. Use the analogy of water pressure to visualise how voltage works.