GCSE Physics - How to Solve: Ohm’s Law and Resistance of a Wire

How to Solve: Ohm’s Law and Resistance of a Wire

Introduction

Master Ohm’s Law and wire resistance, and you’ll crack 5–10% of your GCSE/A-Level Physics exam—plus real-world circuits in phones, cars, and medical devices. One question on this topic appears in every past paper, often worth 4–6 marks. Miss it, and you’re leaving easy points on the table.

WHAT YOU NEED TO KNOW FIRST

Before diving in, ensure you understand:
1. Current (I): Flow of electric charge (measured in amperes, A).
2. Voltage (V): Electrical "push" (measured in volts, V).
3. Resistance (R): Opposition to current flow (measured in ohms, Ω).

If these terms confuse you, pause and review them first—this guide assumes you’re solid on them.

KEY TERMS & FORMULAS

1. Ohm’s Law

Formula: V = I × R - V = Voltage (volts, V) - I = Current (amperes, A) - R = Resistance (ohms, Ω)

MEMORISE THIS. It’s the foundation of circuit problems.

Rearranged versions (also memorise): - I = V / R - R = V / I

2. Resistance of a Wire

Formula: R = (ρ × L) / A - R = Resistance (Ω) - ρ (rho) = Resistivity of the material (Ω·m) – given on exam sheet - L = Length of wire (metres, m) - A = Cross-sectional area (m²)

MEMORISE THIS. Examiners love testing how wire dimensions affect resistance.

Key Notes: - Resistivity (ρ): A property of the material (e.g., copper has low ρ, rubber has high ρ). - Area (A): For a circular wire, A = πr² (r = radius) or A = π(d/2)² (d = diameter).

STEP-BY-STEP METHOD

For Ohm’s Law Problems (V, I, R)

1. Read the question carefully. Underline what’s given and what’s asked.
2. Write down the formula: V = I × R (or rearrange if needed).
3. Substitute the known values. Include units.
4. Solve for the unknown. Show every step.
5. Check units and significant figures. Exams deduct marks for sloppy units.

For Wire Resistance Problems (R = ρL/A)

1. Identify given values: ρ, L, A (or diameter/radius to find A).
2. Convert units if needed:
3. Length → metres (e.g., 50 cm = 0.5 m).
4. Diameter → radius (divide by 2).
5. Area → m² (e.g., 1 mm² = 1 × 10⁻⁶ m²).
6. Calculate area (if not given):
7. A = πr² or A = π(d/2)².
8. Plug into R = (ρ × L) / A.
9. Solve and check units. Resistance should be in ohms (Ω).

WORKED EXAMPLES

Example 1 – Basic Ohm’s Law

Question: A circuit has a current of 2 A and a resistance of 5 Ω. What is the voltage?

Solution:
1. Given: I = 2 A, R = 5 Ω. Find V.
2. Formula: V = I × R
3. Substitute: V = 2 A × 5 Ω
4. Calculate: V = 10 V
5. Answer: 10 V

What we did and why: We used Ohm’s Law directly because voltage was the unknown. No rearranging needed—just plug and solve.

Example 2 – Medium (Rearranged Ohm’s Law)

Question: A 12 V battery is connected to a resistor. The current is 3 A. What is the resistance?

Solution:
1. Given: V = 12 V, I = 3 A. Find R.
2. Rearrange formula: R = V / I
3. Substitute: R = 12 V / 3 A
4. Calculate: R = 4 Ω
5. Answer: 4 Ω

What we did and why: We rearranged Ohm’s Law to solve for resistance. Always check if the formula needs flipping before substituting.

Example 3 – Exam-Style (Wire Resistance)

Question: A copper wire has a length of 2 m and a diameter of 0.5 mm. The resistivity of copper is 1.68 × 10⁻⁸ Ω·m. Calculate its resistance.

Solution:
1. Given: - L = 2 m - Diameter (d) = 0.5 mm = 0.0005 m - ρ = 1.68 × 10⁻⁸ Ω·m
2. Find radius: r = d / 2 = 0.0005 m / 2 = 0.00025 m
3. Calculate area (A): A = πr² = π × (0.00025 m)² = 1.96 × 10⁻⁷ m²
4. Plug into R = (ρ × L) / A: R = (1.68 × 10⁻⁸ Ω·m × 2 m) / 1.96 × 10⁻⁷ m²
5. Calculate: R = (3.36 × 10⁻⁸) / (1.96 × 10⁻⁷) = 0.171 Ω
6. Answer: 0.171 Ω

What we did and why: We converted diameter to radius, calculated area, then used the wire resistance formula. Unit conversion is critical here—examiners love to test it.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP

(Spoken naturally, as if to a student the night before the exam.)

"Okay, listen up—this is your 60-second Ohm’s Law and wire resistance cheat sheet. First, Ohm’s Law: V = I × R. Voltage equals current times resistance. If you forget, draw a triangle—V on top, I and R on the bottom. Cover the one you’re solving for, and the formula appears. Need resistance? R = V/I. Need current? I = V/R.

For wire resistance, remember R = (ρ × L) / A. Resistivity (ρ) is given—don’t memorise it. Length must be in metres, area in m². If they give diameter, halve it for radius, then use A = πr². Convert units first—examiners love to trick you here.

Common mistakes? Forgetting units, mixing up diameter and radius, and not rearranging formulas. Exam traps? Non-ohmic components (don’t use V = IR!), hidden unit conversions, and circuit questions (Ohm’s Law is for single resistors).

You’ve got this. Write down the formulas, convert units, plug in numbers, and check your answer. Now go ace that exam!"