define the potential difference across a component as the energy transferred per unit charge

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Potential Difference and Power – Cambridge A-Level Physics 9702

Potential Difference and Power

Learning Objective

Define the potential difference across a component as the energy transferred per unit charge.

Key Concepts

  • Electric potential (V)
  • Potential difference (ΔV)
  • Energy transferred (ΔE)
  • Charge (Q)
  • Electrical power (P)

Definition of Potential Difference

The potential difference between two points A and B in an electric circuit is the amount of energy transferred to a charge as it moves from A to B, divided by the magnitude of the charge:

$$\Delta V = \frac{\Delta E}{Q}$$

where

  • $\Delta V$ is the potential difference (volts, V)
  • $\Delta E$ is the energy transferred (joules, J)
  • $Q$ is the charge (coulombs, C)

Relationship with Work Done

If a charge $Q$ moves through a component and the electric field does work $W$ on it, then $W = \Delta E$ and the potential difference can also be written as:

$$\Delta V = \frac{W}{Q}$$

Units

Quantity Symbol SI Unit Definition
Potential difference $\Delta V$ volt (V) 1 V = 1 J · C⁻¹
Energy $\Delta E$ joule (J) 1 J = 1 N·m
Charge $Q$ coulomb (C) 1 C = 1 A·s

Electrical Power

Power is the rate at which energy is transferred. For an electric component:

$$P = \frac{\Delta E}{t}$$

Using the definition of potential difference, this can be expressed as:

$$P = \frac{\Delta V \, Q}{t} = \Delta V \, I$$

where $I = Q/t$ is the current (amperes, A).

Worked Example

  1. Calculate the potential difference across a resistor if $2.5\ \text{J}$ of energy is transferred to a charge of $5.0\times10^{-3}\ \text{C}$.
  2. Solution:

Using $\Delta V = \Delta E / Q$:

$$\Delta V = \frac{2.5\ \text{J}}{5.0\times10^{-3}\ \text{C}} = 5.0\times10^{2}\ \text{V}$$

The potential difference is $500\ \text{V}$.

Common Misconceptions

  • Confusing potential difference with the total energy transferred. The potential difference is energy per unit charge, not the total energy.
  • Assuming that a higher voltage always means more power. Power also depends on the current: $P = \Delta \cdot I$.
Suggested diagram: A simple circuit showing a battery, a resistor, and the direction of charge flow, with labels for ΔV across the resistor and the work done on the charge.

Summary

• Potential difference $\Delta V$ is defined as the energy transferred per unit charge, $\Delta V = \Delta E/Q$.
• The SI unit of potential difference is the volt (V), where $1\ \text{V}=1\ \text{J·C}^{-1}$.
• Electrical power can be written as $P = \Delta \cdot I$, linking voltage, current, and the rate of energy transfer.