Question

The power factor at resonance in a parallel R-L-C circuit is_______.

• A. zero
• B. 0.8 lagging
• C. 0.8 leading
• D. unity

Hint:

In both series and parallel RLC circuits, power factor is unity at resonance because voltage and current are in phase.

Answer 1

The Correct Option is D

Step 1: Understand power factor (PF).
Power factor is defined as: \[ \text{PF} = \cos(\phi) \] where $\phi$ is the phase angle between voltage and current.
Step 2: What happens at resonance?
In a parallel RLC circuit, resonance occurs when the inductive and capacitive reactances cancel out: \[ X_L = X_C \Rightarrow \omega L = \frac{1}{\omega C} \] At resonance, the imaginary part of total admittance becomes zero, meaning the circuit behaves like a pure resistor — voltage and current are in phase.
Step 3: Power factor at resonance.
Since $\phi = 0^\circ$ at resonance, \[ \text{PF} = \cos(0) = 1 \] Conclusion: The power factor at resonance is $\boxed{\text{unity}}$.