An alternating voltage V ( t ) = 220 (100 ) volt is applied to a...

$i = \dfrac{V}{R} = \dfrac{220}{50}\sin \left(100\pit\right)$
$\text{i} = {i}_\maxsin \left(100\pit\right)$
For \text{i} = \dfrac{{i}_\max}{2}:
\dfrac{{i}_\max}{2} = {i}_\maxsin \left(100\pi t\right)
$\sin 100\pit = \dfrac{1}{2} ⇒ 100\pit = \dfrac{\pi}{6}$
$t = \dfrac{1}{600}s$
For i = {i}_\max:
{i}_\max = {i}_\maxsin \left(100\pi t\right)
$\sin 100\pit = 1 ⇒ 100\pit = \dfrac{\pi}{2}$
$⇒ t = \dfrac{1}{200}s$

so time for \dfrac{{i}_\max}{2}to{i}_\max is
{t}_{( {i}_\max )} - {t}_{\left(\dfrac{{i}_\max}{2}\right)} = \dfrac{1}{200} - \dfrac{1}{600} = \dfrac{1}{300} = 3.33m{s}^{}