IGCSE Physics - 4.2.3 Electromotive Force and Potential Difference

Objective

Recall and use the equation for potential difference: $V = \frac{W}{Q}$

Understanding Potential Difference (P.D.)

Potential difference, often referred to as voltage, is the difference in electrical potential energy per unit charge between two points in a circuit. It's what drives the flow of electric current.

The unit of potential difference is the volt (V).

The Equation: $V = \frac{W}{Q}$

Where:

• V represents the potential difference (in volts).
• W represents the work done (in joules).
• Q represents the quantity of charge (in coulombs).

This equation states that the potential difference between two points is equal to the amount of work done to move a unit positive charge between those points, divided by the magnitude of that unit charge.

Derivation (Conceptual Understanding)

Imagine moving a charge q from a point with a potential V₁ to a point with a potential V₂. The work done (W) is given by:

$$W = q \times (V_2 - V_1)$$

The potential difference (V) is defined as the difference in electric potential between the two points:

$$V = V_2 - V_1$$

Substituting this into the work equation, we get:

$$W = q \times V$$

Rearranging to solve for V, we obtain the equation:

$$V = \frac{W}{q}$$

For a unit positive charge (q = 1 Coulomb), the equation becomes:

$$V = \frac{W}{1} = W$$

Therefore, the potential difference is equal to the work done per unit charge.

Applications and Examples

1. Battery in a Circuit: A battery converts chemical energy into electrical energy. When a charge flows through the battery, work is done on the charge, increasing its potential energy. This results in a potential difference across the battery terminals.
2. Voltage in a Household Circuit: The voltage supplied by the power outlet (e.g., 230V in the UK) is the potential difference across the circuit. This voltage drives the current through the appliances.
3. Work Done by a Force: If a force (F) moves a charge (Q) a distance (d) in the presence of an electric field, the work done (W) is given by: $$W = F \times d$$. This work is related to the potential difference.

Table Summary

Quantity	Symbol	Unit	Definition
Potential Difference	V	Volt (V)	The difference in electrical potential energy per unit charge between two points.
Work Done	W	Joule (J)	The energy transferred when a force causes displacement.
Quantity of Charge	Q	Coulomb (C)	The fundamental unit of electric charge.