Question

Alternating current in circuit is given by $I=I_0\sin 2\pi nt$ .Then the time taken by the current to rise from zero to r.m.s. value is equal to.

• A. 1/2n
• B. 1/n
• C. 1/4n
• D. 1/8n

Answer 1

Answer: (D)

Alternating current is given as $i=i_0\sin (2\pi nt)$
Rms value of current $i_{rms}=\frac{i_o}{\sqrt{2}}$
Let time taken to reach zero to r.m.s value be t.
$\therefore \frac{i_0}{\sqrt{2}}=i_0\sin (2\pi nt)$
Or $\sin \frac{\pi }{4}=\sin (2\pi nt)$
Or $\frac{\pi }{4}=2\pi nt$
$\Rightarrow t=\frac{1}{8n}$