Question

The variation of instantaneous sinusoidal current $I$ and instantaneous sinusoidal emf $E$ in a circuit is as shown in figure. Which of the following statements are correct?

• A. The emf lags behind the current by $\frac{\pi }{2}$.
• B. The current lags behind the emf by$\frac{\pi }{2}$.
• C. The emf and the current are in phase.
• D. The emf lags behind the current by $\pi$.

Answer 1

The correct option is B The current lags behind the emf by$\frac{\pi }{2}$.


From the graph, we can say that $E$ and $I$ both are following a sine curve, having same frequency.

Now, at $\omega t=0$,

$E=0$ and $I=-I_0$

at $\omega t=\frac{\pi }{2}$

$E=E_0$ and $I=0$

$\therefore$ Their equations are given by,

$E=E_0\sin \omega t$

$I=I_0\sin (\omega t-\frac{\pi }{2})$

Considering the phase in both the equations, it is clear that the current $\left(I\right)$ is lagging the emf $E$ by $\frac{\pi }{2}$.

Hence, $\left(B\right)$ is the correct answer.