The current flowing through an ac circuit is given by $$I = 5\sin(120\pi t)$$ A. How long will the current take to reach the peak value starting from zero?

Given: $$I = 5\sin(120\pi t)$$ A.

Comparing with the standard form $$I = I_0 \sin(\omega t)$$:

$$\omega = 120\pi \text{ rad/s}$$

The current starts from zero (at $$t = 0$$, $$I = 0$$) and reaches its peak value when $$\sin(120\pi t) = 1$$.

$$120\pi t = \frac{\pi}{2}$$

$$t = \frac{\pi}{2 \times 120\pi} = \frac{1}{240} \text{ s}$$

The correct answer is Option D.

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