Question

The time required for a $50Hz$ alternating current to increase from zero to $0.707\%$ of its peak value is -

• A. $2.5ms$
• B. $10ms$
• C. $20ms$
• D. $14.14ms$

Answer 1

The correct option is A $2.5ms$

$i=i_o\sin \left(wt\right)$

$\Rightarrow i=i_o\sin \left(100\pi t\right)$

$\Rightarrow 0.707i_o=i_o\sin \left(100\pi t\right)$

$\Rightarrow \frac{1}{\sqrt{2}}=\sin \left(100\pi t\right)$

$\Rightarrow 100\pi t=\frac{\pi }{4}$

$\Rightarrow t=\frac{1}{400}$

$\Rightarrow t=2.5ms$

Hence,

option $\left(A\right)$ is correct answer.