CSLB C-10 Electrical ContractorElectrical Theory and CalculationsMedium

A parallel circuit has three resistors: R1 = 60 ohms, R2 = 30 ohms, and R3 = 20 ohms. What is the total equivalent resistance of this parallel combination?

  1. A600 ohms
  2. B5 ohms
  3. C110 ohms
  4. D10 ohms
Show answer & explanation

Correct answer: D. 10 ohms

For parallel resistors, the reciprocal of the total resistance is the sum of the reciprocals: 1/Rt = 1/R1 + 1/R2 + 1/R3. So, 1/Rt = 1/60 + 1/30 + 1/20 = 1/60 + 2/60 + 3/60 = 6/60 = 1/10. Therefore, Rt = 10 ohms.

Why the other options are wrong

  • A. This is a significantly incorrect value, possibly from multiplying resistances instead of using reciprocals.
  • B. This is a common error, possibly from incorrect addition of fractions or calculation.
  • C. This would be the total resistance if the resistors were in series.

Parallel Resistive Circuit (Total Resistance)

In a parallel resistive circuit, the reciprocal of the total equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

  • Formula: 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn.
  • The total resistance in a parallel circuit is always less than the smallest individual resistance.
  • For two resistors: Rt = (R1 * R2) / (R1 + R2).
  • Voltage is the same across all branches.

Memory trick: Reciprocal sum for parallel, less than the smallest for all.

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