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(A) The average value of current $I$ over a time interval $[t_1, t_2]$ is given by $I_{av} = \frac{1}{t_2 - t_1} \int_{t_1}^{t_2} I \, dt$.Here,$t_1 =

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$\frac{2I_0}{\pi}$

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(A) The average value of current $I$ over a time interval $[t_1, t_2]$ is given by $I_{av} = \frac{1}{t_2 - t_1} \int_{t_1}^{t_2} I \, dt$.Here,$t_1 = 0$ and $t_2 = \frac{\pi}{\omega}$.$I_{av} = \frac{1}{\frac{\pi}{\omega} - 0} \int_0^{\frac{\pi}{\omega}} I_0 \sin \omega t \, dt$$I_{av} = \frac{\omega}{\pi} I_0 \left[ \frac{-\cos \omega t}{\omega} \right]_0^{\frac{\pi}{\omega}}$$I_{av} = \frac{I_0}{\pi} [-\cos(\omega \cdot \frac{\pi}{\omega}) - (-\cos(0))]$$I_{av} = \frac{I_0}{\pi} [-\cos(\pi) + \cos(0)]$$I_{av} = \frac{I_0}{\pi} [-(-1) + 1] = \frac{I_0}{\pi} [1 + 1] = \frac{2I_0}{\pi}$.

The average value of alternating current $I = I_0 \sin \omega t$ in the time interval $[0, \frac{\pi}{\omega}]$ is:

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