What is the power factor angle of an RC series circuit?

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SSC JE Electrical 16 Nov 2022 Shift 3 Official Paper
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  1. tan-1 \((\frac{1}{WCR})\)
  2. tan-1 \((\frac{CR}{W})\)
  3. tan-1\((\frac{R}{CW})\)
  4. tan-1\((\frac{W}{CR})\)

Answer (Detailed Solution Below)

Option 1 : tan-1 \((\frac{1}{WCR})\)
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Detailed Solution

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Concept:
Impedance triangle for the series RC circuit

F1 Nakshatra Madhu 19.10.21  D2

Impedance triangle for series RL circuit
F1 Nakshatra Madhu 19.10.21 D1


Calculation:

Power factor=  \(cos(\theta )\)

Where power factor angle

By the Impedance triangle of the series RC circuit, we can write

\(tan(\theta)=\frac{Opposite}{Adjucent}=\frac{X_c}{R}\)

\(Therefore \ Power\ factor \ angle \ \theta =tan^{-1}(\frac{1}{\omega RC})\)

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