For an AC circuit, a phase diagram shows emf on X-axis, and current I is at angle \( \theta \) to emf. Angle is phase angle \( \theta \) between emf and current. Current I is resolved into two components, \( I\cos\theta \) is along emf on X-axis. \( I\sin\theta \) is along perpendicular direction to emf.
(A) Component \( I\cos\theta \) will draw the power from the source
(B) Component \( I\sin\theta \) will draw the power from the source
(C) \( I\cos\theta \) is called the powerless current
(D) \( I\sin\theta \) is called the powerless current
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) and (D) only
The average power in an ac circuit is
\( \displaystyle P = V_{\mathrm{rms}}\,I_{\mathrm{rms}}\cos\theta = V_{\mathrm{rms}}\,(I_{\mathrm{rms}}\cos\theta) \)
So only the component of current in phase with the emf, \( I\cos\theta \), carries power. The component \( I\sin\theta \) is \( 90^\circ \) out of phase with the emf, and the average power of a voltage and a current differing in phase by \( 90^\circ \) is zero (\( \cos 90^\circ = 0 \)). This component is the wattless (powerless) current.
(A) Component \( I\cos\theta \) will draw the power from the source — Correct. It is in phase with the emf, and all the average power is drawn by this component.
(B) Component \( I\sin\theta \) will draw the power from the source — Incorrect. Being \( 90^\circ \) out of phase with the emf, it draws zero average power.
(C) \( I\cos\theta \) is called the powerless current — Incorrect. This is the component that draws the power.
(D) \( I\sin\theta \) is called the powerless current — Correct. It is the wattless current.
NCERT (2026-27):
Power in AC Circuit: The Power Factor – “… 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. IP is known as the power component because it is in phase with the voltage and corresponds to power loss in the circuit.”