If I_1, I_2, I_3 and I_4 are the respective r | vedclass

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(B) The $r.m.s.$ value of a current is defined as $I_{rms} = \sqrt{\frac{1}{T} \int_0^T i^2 dt}$.For case $I$ and $II$,the current is a rectified sine

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$I_3 > I_1 = I_2 > I_4$

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(B) The $r.m.s.$ value of a current is defined as $I_{rms} = \sqrt{\frac{1}{T} \int_0^T i^2 dt}$.For case $I$ and $II$,the current is a rectified sine wave: $i = |I_0 \sin(\omega t)|$. The $r.m.s.$ value is $I_1 = I_2 = \frac{I_0}{\sqrt{2}} \approx 0.707 I_0$.For case $III$,the current is a square wave: $i = I_0$ for half cycle and $-I_0$ for the other half. The $r.m.s.$ value is $I_3 = \sqrt{\frac{1}{T} (I_0^2 \cdot \frac{T}{2} + (-I_0)^2 \cdot \frac{T}{2})} = I_0$.For case $IV$,the current is a triangular wave: $i = \frac{2I_0}{T} t$ for $0 Comparing the values: $I_3 = I_0$,$I_1 = I_2 = 0.707 I_0$,and $I_4 = 0.577 I_0$.Thus,the correct relation is $I_3 > I_1 = I_2 > I_4$.

If $I_1, I_2, I_3$ and $I_4$ are the respective $r.m.s.$ values of the time-varying currents as shown in the four cases $I, II, III$ and $IV$,then identify the correct relation.

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