In an ac circuit containing only an inductor, the period of the ac is T. If the voltage across the inductor is maximum at time \( t=2T \), at what time does the current next reach its maximum value?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 9T/4 \)
In an ac circuit with only an inductor, the current lags the voltage by \( \pi/2 \), that is, by one quarter of a cycle. So each maximum of the current comes a time \( T/4 \) after the corresponding maximum of the voltage.
The voltage is maximum at \( t=2T \), so the current next reaches its maximum at:
\( \begin{aligned} t &= 2T+\frac{T}{4} \\ &= \frac{9T}{4} \end{aligned} \)
NCERT (2026-27):
AC Voltage Applied to an Inductor – “A comparison of Eqs. (7.1) and (7.12) for the source voltage and the current in an inductor shows that the current lags the voltage by π/2 or one-quarter (1/4) cycle.”
\( v=v_m\sin\omega t \qquad (7.1) \)
\( \displaystyle i=i_m\sin\left(\omega t-\frac{\pi}{2}\right) \qquad (7.12) \)