Physics - EMI/AC Question with Solution | TestHub

$i=\frac{V}{R}=\frac{220}{50}\sin \left(100\pi t\right)$
$\text{i}=i_{max}\sin \left(100\pi t\right)$
For $\text{i}=\frac{i_{max}}{2}:$
$\frac{i_{max}}{2}=i_{max}\sin \left(100\pi t\right)$
$$\begin{gathered} \sin 100\pi t=\frac{1}{2} \\ \Rightarrow 100\pi t=\frac{\pi }{6} \end{gathered}$$
$t=\frac{1}{600}\text{s}$
For $i=i_{max}:$
$i_{max}=i_{max}\sin \left(100\pi t\right)$
$\sin 100\pi t=1\Rightarrow 100\pi t=\frac{\pi }{2}$
$\Rightarrow t=\frac{1}{200}\text{s}$

so time for $\frac{i_{max}}{2}to{i}_{max}$ is
$t_{(i_{max})}-t_{\left(\frac{i_{max}}{2}\right)}=\frac{1}{200}-\frac{1}{600}=\frac{1}{300}=3.33m{\text{s}}^{}$