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Sensing

Series and parallel combinations

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on combining resistances and conductances in series and in parallel, why a parallel combination has less resistance than its smallest branch, calculating combined resistances and branch currents, mixed series and parallel networks, current dividing in inverse proportion to resistance, and why household appliances are wired in parallel.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

Calculate the combined resistance of 4.0 Ω and 6.0 Ω in series.

Numbers

Calculate the combined resistance of 4.0 Ω and 6.0 Ω in parallel.

Key term

Explain why the resistance of a parallel combination is always smaller than the smallest resistance in it.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State how resistances combine in series.

    Model answer

    They add directly, so R = R₁ + R₂ + … for any number of resistors in series.

  2. 2

    State how resistances combine in parallel.

    Model answer

    Their reciprocals add, so 1/R = 1/R₁ + 1/R₂ + … for any number of resistors in parallel.

  3. 3

    State how conductances combine in parallel.

    Model answer

    They add directly, so G = G₁ + G₂ + … for any number of components in parallel.

  4. 4

    State how conductances combine in series.

    Model answer

    Their reciprocals add, so 1/G = 1/G₁ + 1/G₂ + … for any number of components in series.

  5. 5

    Calculate the combined resistance of 4.0 Ω and 6.0 Ω in series.

    Model answer

    The combined resistance is 10 Ω.

  6. 6

    Calculate the combined resistance of 4.0 Ω and 6.0 Ω in parallel.

    Model answer

    The conductances add to 0.25 + 0.167 = 0.417 S, so the resistance is 2.4 Ω.

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