Question

Power factor of the following circuit will be zero

• A. Resistance
• B. Inductance
• C. Capacitance
• D. Both (b) and (c)

Hint:

Pure resistor has power factor 1. Pure inductor and pure capacitor have power factor 0.

Answer 1

The Correct Option is D

Concept:
Power factor in an AC circuit is defined as: \[ \cos\phi \] where \(\phi\) is the phase angle between voltage and current. The average power consumed in an AC circuit is: \[ P=V_{\text{rms}}I_{\text{rms}}\cos\phi \] If: \[ \cos\phi=0 \] then average power consumed is zero.

Step 1: Power factor in pure resistance.
In a pure resistor, voltage and current are in the same phase. So: \[ \phi=0^\circ \] \[ \cos0^\circ=1 \] Therefore, power factor of pure resistance is 1.

Step 2: Power factor in pure inductance.
In a pure inductor, current lags behind voltage by: \[ 90^\circ \] So: \[ \phi=90^\circ \] \[ \cos90^\circ=0 \] Thus, power factor of pure inductance is zero.

Step 3: Power factor in pure capacitance.
In a pure capacitor, current leads voltage by: \[ 90^\circ \] Again: \[ \phi=90^\circ \] \[ \cos90^\circ=0 \] So power factor of pure capacitance is also zero.

Step 4: Check the options.
Option (A) Resistance is incorrect because power factor is 1.
Option (B) Inductance has zero power factor.
Option (C) Capacitance has zero power factor.
Option (D) Both inductance and capacitance is correct. Hence, the correct answer is: \[ \boxed{(D)\ \text{Both (b) and (c)}} \]