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Variation of current with time is shown in below. Choose the correct statement(s).

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Mean value of current for one complete cycle zero.

Mean value of current for one complete cycle is $\frac{3}{4} I_{0}$ .

rms value of current is $\frac{I_{0}}{\sqrt{3}} .$

rms value of current $\sqrt{\frac{2}{3}} I_{0}$ .

answer is B, D.

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Detailed Solution

$\begin{array}{l} mean = \frac{Area under I - t curve}{time int erval} = \frac{3 I_{0}}{4} \\ I_{rms} = \sqrt{\frac{\int_{0}^{T / 2} I_{1}^{2} dt + \int_{T / 2}^{T} I_{2}^{2} dt}{\int_{0}^{T} dt}} \end{array}$

Where $I_{1} = I_{0}$ when $0 < t < T / 2$

$I_{2} = - \frac{2 I_{0}}{T} t + 2 I_{0}$ when $T / 2 < t < T$

By solving, $I_{rms} = I_{0} \sqrt{\frac{2}{3}}$

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