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Series and parallel circuits practice

Series components share one current path. Parallel branches connect across the same pair of nodes and therefore share a voltage difference. Identify the circuit structure before calculating.

By ExamCat · Original study lesson · Published September 24, 2026

Understand the method

Series resistances add. For parallel resistors, reciprocal resistances add. In an ideal circuit, current entering a junction equals current leaving it; the battery does not force identical current through unequal parallel branches.

Worked example, step by step

Connect 6 Ω and 3 Ω resistors in parallel across an ideal 12 V source.

  1. Calculate equivalent resistance: 1/R = 1/6 + 1/3 = 1/2, so R = 2 Ω.
  2. The 6 Ω branch carries 12/6 = 2 A.
  3. The 3 Ω branch carries 12/3 = 4 A.
  4. Total current is 6 A, matching 12 V/2 Ω. The smaller branch resistance carries the larger current.

A mistake to watch for

Adding 6 + 3 gives the series equivalent, not the parallel equivalent. For positive finite resistances in parallel, the equivalent is smaller than the smallest individual resistance.

Try it yourself: three questions

Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.

1. Put 6 Ω and 3 Ω in series across 18 V. Find current.

Show answer and explanation

Equivalent resistance is 9 Ω, so current is 2 A through both resistors.

2. In that series circuit, what voltage is across 6 Ω?

Show answer and explanation

V = 2 × 6 = 12 V. The other resistor has 6 V, adding to the 18 V source.

3. Two equal 8 Ω resistors are in parallel. Find equivalent resistance.

Show answer and explanation

4 Ω. Two equal current paths double conductance, which halves equivalent resistance.

Build your next practice session

Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.

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Further reading

OpenStax Physics provides textbook background. The worked scenario and practice questions on this page were written independently for ExamCat.

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