AS · Practice questions · Kirchhoff laws

Charge and energy balance.

Six original Cambridge-style questions on both Kirchhoff laws and series and parallel resistors.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Add, or add reciprocals.

First law: currents balance at a junction.
Series: R = R₁ + R₂.
Parallel: 1/R = 1/R₁ + 1/R₂.

Analysis

[2 marks]

State Kirchhoff first and second laws.

First law: the total current into a junction equals the total current out (conservation of charge) ✓
Second law: around any closed loop, the sum of the e.m.f.s equals the sum of the p.d.s (conservation of energy) ✓

Analysis

[2 marks]

Resistors of 2.0 Ω, 3.0 Ω and 5.0 Ω are connected in series. Find the combined resistance.

In series the resistances add ✓
R = 2.0 + 3.0 + 5.0 = 10 Ω ✓

Analysis

[2 marks]

Two 4.0 Ω resistors are connected in parallel. Find the combined resistance.

1/R = 1/4.0 + 1/4.0 = 1/2.0 ✓
R = 2.0 Ω ✓

Analysis

[3 marks]

A 12 V supply is connected across a 3.0 Ω and a 6.0 Ω resistor in series. Find the current and the p.d. across the 6.0 Ω resistor.

Total R = 9.0 Ω; I = 12/9.0 = 1.33 A ✓
V = IR = 1.33 × 6.0 = 8.0 V ✓

Analysis

[2 marks]

At a junction a current of 5.0 A flows in. It divides into two branches, one carrying 2.0 A. Find the current in the other branch.

By the first law the currents out must total 5.0 A ✓
Other branch = 5.0 − 2.0 = 3.0 A ✓

Analysis

[3 marks]

A 6.0 Ω resistor is in series with a parallel pair of 4.0 Ω resistors, across a 16 V supply. Find the total resistance and the current from the supply.

Parallel pair: 1/R = 1/4.0 + 1/4.0 = 1/2.0, so 2.0 Ω ✓
Total = 6.0 + 2.0 = 8.0 Ω; I = 16/8.0 = 2.0 A ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.