Question

Alternating current in circuit is given by $I=I_{0}sin2\pi nt$. Then the time taken by the current to rise from zero to r.m.s. value is equal to

• A. $\frac{1}{2n}$
• B. $\frac{1}{n}$
• C. $\frac{1}{4n}$
• D. $\frac{1}{8n}$

Answer 1

The correct option is D $\frac{1}{8n}$

Alternating current is given as $i=i_{0}sin\left(2\pi nt\right)$
Rms value of current $i_{rms}=\frac{i_o}{\sqrt{2}}$
Let time taken to reach zero to r.m.s value be $t$.
$\therefore$ $\frac{i_o}{\sqrt{2}}=i_{o}sin\left(2\pi nt\right)$

Or $sin\frac{\pi }{4}=sin\left(2\pi nt\right)$
Or $\frac{\pi }{4}=2\pi nt$

$⟹t=\frac{1}{8n}$