Question

In an $AC$ circuit, the current is given by $I=4\sin (100\pi t+{30}^{\circ })\text{A}$. The current becomes maximum for the first time $(\text{After}t=0)$ at $t$ equal to

• A. $\frac{1}{200}\text{s}$
• B. $\frac{1}{300}\text{s}$
• C. $\frac{1}{50}\text{s}$
• D. $\frac{1}{100}\text{s}$

Answer 1

The correct option is B $\frac{1}{300}\text{s}$

Given:
$I=4\sin (100\pi t+{30}^{\circ })......\left(1\right)$

From the above equation, the maximum value of current is given by,
$I_0=4$

Substituting $I=4$ in $\left(1\right)$, we get

$\sin (100\pi t+{30}^{\circ })=1$

$\Rightarrow 100\pi t+\frac{\pi }{6}=\frac{(2n+1)\pi }{2}$

For minimum value of $t$, $n=0$

$\Rightarrow 100\pi t=\frac{\pi }{3}$

$\Rightarrow t=\frac{1}{300}\text{s}$

Hence, option $\left(B\right)$ is correct.