Question

If alternating current in a circuit is given by. $I=I_0\sin 2\pi nt$, then the time taken by the current to charge from rms value to zero is equal to.

• A. $\left(1/n\right)$
• B. $\left(1/2n\right)$
• C. $\left(1/4n\right)$
• D. $\left(1/8n\right)$

Answer 1

Answer: (D)

$\left(1/8n\right)$

$\text{Given:-}I=I_{0}sin2\pi nt$

$\text{Solution:-}$

We have given,

$I=I_{0}sin2\pi nt$

Here,

$I=I_{rms}$

And we know that,

$\Rightarrow I_{rms}=\frac{I_0}{\sqrt{2}}$

So the equation become,

$\frac{I_0}{\sqrt{2}}=I_{0}sin2\pi nt$

$\frac{1}{\sqrt{2}}=sin\left(2\pi nt\right)$

$si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)=2\pi nt$

$\frac{\pi }{4}=2\pi nt$

$\Rightarrow t=\frac{1}{8n}$

$\text{Hence the correct option is D}$