Potential Difference Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Potential Difference.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The difference in electric potential between two points, equal to the work done per unit charge moving between them.

Potential difference is the 'height drop' that makes charges flow — the bigger the drop, the harder the push.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Potential difference is what actually drives current in circuits — it's the 'voltage' engineers measure.

Common stuck point: Voltage is always measured between two points — saying 'the voltage at this wire' implicitly means relative to ground.

Sense of Study hint: When solving a potential difference problem, identify the two points you are comparing. First, find the electric potential at each point (or the work done moving a charge between them). Then subtract: \Delta V = V_B - V_A. Finally, use \Delta V = W/q to relate voltage to energy and charge.

Worked Examples

Example 1

easy
A battery has a potential difference of 9 \text{ V} across its terminals. How much energy does it give to each coulomb of charge that passes through it?

Solution

  1. 1
    Potential difference (voltage) is defined as energy per unit charge: V = \frac{W}{Q}.
  2. 2
    For 1 \text{ C} of charge: W = VQ = 9 \times 1 = 9 \text{ J}.
  3. 3
    Each coulomb of charge gains 9 \text{ J} of electrical energy from the battery.

Answer

W = 9 \text{ J per coulomb}
Potential difference measures the energy transferred per unit charge between two points. A 9 \text{ V} battery gives 9 \text{ J} of energy to every coulomb of charge, which is then dissipated in the circuit components.

Example 2

medium
A current of 0.5 \text{ A} flows through a 10 \text{ } \Omega resistor. What is the potential difference across the resistor? How much energy is dissipated in 20 \text{ s}?

Example 3

medium
A 12 \text{ V} battery drives 3 \text{ A} of current through a resistor. Find the resistance and the power dissipated.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Two points A and B in an electric field have potentials V_A = 100 \text{ V} and V_B = 40 \text{ V}. What is the potential difference from A to B? How much work is done moving a 2 \times 10^{-6} \text{ C} charge from B to A?

Example 2

hard
In a circuit with a 12 \text{ V} battery, three resistors in series have values 2 \text{ } \Omega, 4 \text{ } \Omega, and 6 \text{ } \Omega. What is the potential difference across each? Verify that they sum to the battery voltage.
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Related Concepts

Electric PotentialVoltage

Background Knowledge

These ideas may be useful before you work through the harder examples.

electric potentialvoltage