4.2.3 Electromotive force and Potential Difference

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

Potential Difference (p.d.)

Potential difference (p.d.) is a fundamental concept in electricity. It represents the difference in electrical potential between two points. It's essentially the 'push' that drives electric current through a circuit.

We define potential difference as the work done per unit charge in moving a charge between two points.

Mathematically, potential difference is represented by the symbol (V) and is defined as:

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

Where:

• V = Potential Difference (in Volts)
• W = Work done (in Joules)
• Q = Charge (in Coulombs)

This equation states that the potential difference between two points is equal to the amount of work required to move one Coulomb of charge between those points.

Units of Potential Difference

The unit of potential difference is the Volt (V). One Volt is defined as one Joule of work done per Coulomb of charge.

Relationship with Electric Potential

Potential difference is often referred to as electric potential difference. It's related to the electric potential at a point. The electric potential (V) at a point is the electric potential energy per unit charge at that point. The potential difference between two points is the difference in electric potential between those two points.

Example

Consider a circuit where a battery is used to drive current. The battery provides a potential difference between its positive and negative terminals. This potential difference causes electrons to flow through the circuit.

Table Summary

Concept	Definition	Symbol	Unit
Potential Difference	Work done per unit charge in moving a charge between two points.	V	Volt (V)
Electric Potential	Electric potential energy per unit charge at a point.	V	Volt (V)
Relationship	Potential difference is the difference in electric potential between two points.	ΔV = VB - VA	Volt (V)

Key Points

• Potential difference is a scalar quantity.
• A higher potential difference means a stronger 'push' on the charges in a circuit, leading to a larger current (assuming resistance is constant).
• Batteries provide a constant potential difference.
• The potential difference across a component (like a resistor) is related to the current flowing through it by Ohm's Law.