Question

In List 1, Variation of current $i$ with time $t$ is given in the figure. In List 2, root mean square current $i_{rms}$ and average current are given. Match List 1 with the corresponding quantities given in List 2.

Answer 1

A:
Full cycle average current is zero since ${\int }_0^T\sin \omega tdt=0$, area under the i-t curve is zero for T.
B:
Full cycle average current is zero since ${\int }_0^T\sin \omega tdt=0$
$i_{rms}=\frac{1}{\frac{T}{4}}\sqrt{{\int }_0^{\frac{T}{4}}{i}^{2}dt}=\frac{1}{\frac{T}{4}}\sqrt{{\int }_0^{\frac{T}{4}}(\frac{i_0}{\frac{T}{4}}{)}^2{t}^{2}dt}=\sqrt{i_0^2\left(\frac{4}{T}{)}^3\right(\frac{T}{4}{)}^3\frac{1}{3}}=\frac{i_0}{\sqrt{3}}$
C:
Average current for positive half cycle is $i_{avg}=\frac{1}{\frac{T}{2}}{\int }_0^{\frac{T}{2}}{i}_{0}dt=i_0$
Average current for a full cycle is zero since the area under i-t curve is zero for full cycle T.
D:
Average current for positive half cycle($\frac{T}{2}$) is $i_0$