Class 10 Series and Parallel Resistance: Worked Comparison

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The useful comparison

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Use 4 Ω and 12 Ω across an ideal 12 V supply

In series, the total is 16 Ω and the current is 12/16 = 0.75 A. The drops are 0.75 × 4 = 3 V and 0.75 × 12 = 9 V. They add to 12 V. The larger resistor has the larger voltage drop because the current is shared.

In parallel, 1/R = 1/4 + 1/12 = 1/3, so R = 3 Ω. Branch currents are 12/4 = 3 A and 12/12 = 1 A. The supply current is 4 A. The smaller resistor carries more current because the voltage is shared.

Use node labels on an awkward drawing

A wire drawn as a loop or bent line still connects the same node if there is no intervening component. Label the two ends of each resistor A and B where appropriate. Components connected between the same A and B are parallel even if they are drawn far apart.

Conversely, two resistors drawn side by side are not automatically parallel. If there is a junction between them where current can branch, do not assume their currents must be equal.

Explain the change

The parallel arrangement offers more than one current path and has lower equivalent resistance. With a fixed ideal supply voltage, the supply current is therefore larger. Keep the phrase “fixed voltage” in the explanation; changing the supply condition changes what can be concluded. These are ideal circuit calculations for study, not household wiring instructions.

Check your understanding with a changed example

With an ideal 6 V supply and resistors of 3 Ω and 6 Ω, predict which arrangement draws more supply current. Calculate both arrangements before reading the check below.

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This is a focused learning resource, not a complete chapter or a prediction of board questions. Use your current syllabus and the paper-specific marking scheme for assessment requirements.