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

Published by Patrick Mutisya · 14 days ago

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

QuantitySymbolSI UnitDefinition
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.