9.2 Potential Difference and Power

2026 📋 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Define the potential difference across a component as the energy transferred per unit charge
  2. Recall and use V = W/Q
  3. Recall and use P = VI, P = I²R, and P = V²/R

1. Potential Difference

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What is Potential Difference?

When a battery (or any power supply) is connected to a circuit, it pushes electric charges around the circuit. As these charges move through a component — like a bulb or a resistor — they transfer energy to that component.

Potential difference (p.d.) is the name we give to the measurement of how much energy is transferred by the charge as it passes through a component.

Definition: The potential difference across a component is the energy transferred per unit charge flowing through it.

"Per unit charge" means: for every single coulomb (C) of charge that passes through.

  • Potential difference is also commonly called voltage.
  • It is measured in volts (V).
  • 1 volt = 1 joule per coulomb (1 V = 1 J C⁻¹)

This means: if a bulb has a potential difference of 3 V across it, then every coulomb of charge that flows through the bulb transfers 3 joules of energy to the bulb.

Understanding Potential Difference with an Analogy

Think of electric charge like water flowing through a pipe. The potential difference is like the pressure that pushes the water — the higher the pressure, the more energy each "bit" of water carries as it moves through.

A 240 V mains supply transfers 20 times more energy per coulomb than a 12 V car battery. This is why a 240 V lamp glows far more brightly than a 12 V lamp even if the same amount of charge flows through both every second.

How is Potential Difference Measured?

Potential difference is measured using a device called a voltmeter.

  • A voltmeter is always connected in parallel with the component you are measuring — meaning it is placed across the two ends of the component, not in the main line of the circuit.
  • This allows the voltmeter to measure the difference in electrical potential (energy level) on each side of the component.

Potential Difference in a Series Circuit

When a power supply is connected to several components in series (one after another in a single loop), the total potential difference of the supply is shared among all the components.

Example: A 12 V power supply connected to a bulb and a resistor in series. If the bulb has 5 V across it, the resistor will have 7 V across it — because 5 + 7 = 12 V.

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