$$\Rightarrow$$ i = i₀sin$$\omega$$t

when i = i₀

i₀ = i₀sin$$\omega$$t₁ $$\Rightarrow$$ $$\omega$$t₁ = $${\pi \over 2}$$ ..... (i)

When i = $${{{i_1}} \over {\sqrt 2 }}$$

$${{{i_1}} \over {\sqrt 2 }}$$ = i₀sin$$\omega$$t₂ $$\Rightarrow$$ $$\omega$$t₂ = $${\pi \over 4}$$ ...... (ii)

Time taken by current from maximum value to rms value

$$ \Rightarrow ({t_1} - {t_2}) = {\pi \over {2\omega }} - {\pi \over {4\omega }} = {\pi \over {4\omega }} = {\pi \over {4 \times 2\pi f}}$$

$$ = {1 \over {8 \times 50}}$$

$${1 \over {400}}$$ sec

= 2.5 ms