CSLB C-10 Electrical ContractorElectrical Theory and CalculationsMedium

A technician is testing an AC circuit with a total impedance of 15 ohms and a power factor of 0.8 lagging. If the circuit is supplied by a 120V source, what is the approximate resistance of the circuit?

  1. A9.0 ohms
  2. B12.0 ohms
  3. C15.0 ohms
  4. D7.5 ohms
Show answer & explanation

Correct answer: B. 12.0 ohms

In an AC circuit, the power factor (PF) is the ratio of resistance (R) to impedance (Z). So, PF = R/Z. Given PF = 0.8 and Z = 15 ohms, we can solve for R: R = PF × Z = 0.8 × 15 ohms = 12 ohms.

Why the other options are wrong

  • A. Incorrect calculation, possibly from using a different power factor or misinterpreting the formula.
  • C. This is the total impedance, not the resistance.
  • D. Incorrect calculation, possibly from dividing by 2 or other error.

Resistance from Impedance and Power Factor

In an AC circuit, resistance (R) can be determined from the total impedance (Z) and the power factor (PF) using the relationship R = Z × PF. This comes from the power triangle where PF = cos(θ) = R/Z.

  • PF = R/Z for an AC circuit.
  • Resistance (R) is the real part of impedance.
  • Measured in Ohms (Ω).

Memory trick: Power Factor is R over Z, so Resistance is Z times Power Factor.

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