Question

What will be the phase difference between virtual voltage and virtual current when current in the circuit is wattless?

• A. $60^{\circ}$
• B. $45^{\circ}$
• C. $90^{\circ}$
• D. $180^{\circ}$

Hint:

Wattless current occurs in purely inductive or purely capacitive circuits where voltage and current are $90^{\circ}$ out of phase.

Answer 1

The Correct Option is C

Step 1: The average power ($P_{\text{avg$) consumed in an AC circuit is given by the formula: \[ P_{\text{avg = V_{\text{rms I_{\text{rms \cos \phi \] where $V_{\text{rms$ is virtual voltage, $I_{\text{rms$ is virtual current, and $\phi$ is the phase difference.
Step 2: A current is described as "wattless" when the average power consumed in the circuit is zero. \[ P_{\text{avg = 0 \]
Step 3: For the power to be zero while the voltage and current are non-zero, the power factor ($\cos \phi$) must be zero. \[ \cos \phi = 0 \]
Step 4: The phase difference ($\phi$) that makes the cosine equal to zero is $90^{\circ}$. \[ \phi = 90^{\circ} \]