In an ac circuit, the rms current is 10 A and it lags behind the voltage. The power factor of the circuit is 0.6. The wattless component of the current is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8 A
The current can be split into two parts. The part in phase with the voltage, \( I_p=I\cos\phi \), is the power component. The part at right angles to the voltage, \( I_q=I\sin\phi \), is the wattless component. This part uses no power.
Given:
\( I=10\ \mathrm{A} \)
\( \cos\phi=0.6 \)
\( \begin{aligned} \sin\phi &= \sqrt{1-\cos^{2}\phi} \\ &= \sqrt{1-0.36} \\ &= 0.8 \end{aligned} \)
\( \begin{aligned} I_q &= I\sin\phi \\ &= 10\times0.8 \\ &= 8\ \mathrm{A} \end{aligned} \)
NCERT (2026-27):
Example 7.7 – “… Let us resolve I into two components. Ip along the applied voltage V and Iq perpendicular to the applied voltage. Iq as you have learnt in Section 7.7, is called the wattless component since corresponding to this component of current, there is no power loss. …”