A student sets up two identical resistors, one connected in series with a power supply and one connected in parallel with a second identical resistor across the same power supply. Explain why the total resistance of the parallel arrangement is lower than the total resistance of the series arrangement.

OCR A-Level Physics B: Advancing Physics (H557) — 3.4 Materials · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Two resistors, each with a resistance of 4 Ω, are available. In arrangement A, both resistors are connected in series. In arrangement B, both resistors are connected in parallel.

Model answer (5 marks)

In the series arrangement the total resistance is the sum of the individual resistances: R_total = 4 Ω + 4 Ω = 8 Ω. All the current must pass through both resistors, so the current is limited by both, making it harder for charge to flow.

In the parallel arrangement the current splits between the two 4 Ω branches. Each branch offers a path of 4 Ω, so the overall resistance is lower: 1/R_total = 1/4 Ω + 1/4 Ω = 1/2 Ω, giving R_total = 2 Ω. Because charge can take more than one path, it is easier for current to flow, so the total resistance is less than that of either single resistor.

Thus the parallel arrangement has a lower total resistance than the series arrangement.

Examiner tips

  • Show the series formula R_total = R1+R2 and calculate 8 Ω. Use the parallel formula 1/R_total = 1/R1+1/R2 to get 2 Ω. Explain that current splits, giving more paths and lower resistance. Mention that the parallel resistance is less than the smallest individual resistor.

Common mistakes

  • Calculating the parallel resistance incorrectly (e.g. adding instead of using 1/R). Forgetting to state that current splits in the parallel case. Claiming the series resistance is lower instead of higher.

Mark scheme (5 marks)

  1. In the series arrangement, the total resistance is equal to the sum of the individual resistances
  2. In the series arrangement, all the charge/current must flow through both resistors, making it harder for current to flow
  3. In the parallel arrangement, the current splits so charge has more than one path/branch to take
  4. Because charge can take more than one path, it is easier for current to flow overall, so the total resistance is lower
  5. The total resistance in the parallel arrangement is less than the resistance of either individual resistor / less than the smallest individual resistance

Key terms in this question

series · parallel · total resistance

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