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Difficulty: EasyParallel Circuits

An aircraft instrument panel contains three identical 12 Ω12\ \Omega indicator lights connected in parallel across a direct-current power bus. What is the total equivalent resistance of this parallel circuit?

  1. A
    36 Ω36\ \Omega
  2. B
    12 Ω12\ \Omega
  3. 4 Ω4\ \OmegaAnswer
  4. D
    3 Ω3\ \Omega

Answer

4 Ω4\ \Omega
For parallel circuits containing equal resistors, the total equivalent resistance is found by dividing the individual resistance value by the number of parallel branches (Rtotal=R/NR_{\text{total}} = R / N). Here, 12 Ω/3=4 Ω12\ \Omega / 3 = 4\ \Omega.

Step-by-Step Solution

1
Identify the number of parallel branches and branch resistance
Branch resistance R=12 ΩR = 12\ \Omega, number of branches N=3N = 3
When all resistors in parallel have identical resistance values, the equal-resistor shortcut formula can be directly applied.
2
Calculate total equivalent resistance using Rtotal=RNR_{\text{total}} = \frac{R}{N}
Rtotal=12 Ω3=4 ΩR_{\text{total}} = \frac{12\ \Omega}{3} = 4\ \Omega
Connecting resistors in parallel provides multiple parallel paths for current, reducing the total equivalent resistance below any individual branch.

Key Concept

Equal-Resistor Parallel Shortcut Rule (Rtotal=R/NR_{\text{total}} = R / N)
Estimated Time:45s
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Topics

Parallel Circuits

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