Question

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 $\text{I, II, III}$ and $\text{IV}$. Then identify the correct relations.

• A. $I_2>I_1$
• B. $I_3>I_4$
• C. $I_1>I_4$
• D. $I_1=I_2$

Answer 1

Answer: (B), (C), (D)

$I_1=I_2$

We know that the rms value of current is given by,

$I_{rms}=\sqrt{\frac{1}{T}{\int }_0^T{I}^{2}dt}$

Here, the time period $T$ is the same for all the four cases.

We know that the ${\int }_0^T{I}^{2}dt$ represents the area under $(I^2-t)$ curve in one cycle.

The corresponding $I^2-t$ graphs for each case can be drawn as,


Therefore, from the $I^2-t$ graphs we can conclude that,

$I_3>I_1=I_2>I_4$

Hence, options $\left(B\right),\left(C\right)$ and $\left(D\right)$ are the correct answers.