Question

In an AC circuit, the current is given by the equation, $i=2\sqrt{13}\sin \left(50\pi t\right)\text{A}$. Calculate the time taken to reach from zero $($at $t=0)$ to its first maximum value.

• A. $5\text{ms}$
• B. $10\text{ms}$
• C. $20\text{ms}$
• D. $100\text{ms}$

Answer 1

The correct option is B $10\text{ms}$

Given:

Current, $i=2\sqrt{13}\sin \left(50\pi t\right)\text{A}$

Comparing with $i=i_0\sin \omega t$, we get, angular frequency,

$\omega =50\pi \text{rad/s}$

So, time period,

$T=\frac{2\pi }{\omega }=\frac{2\pi }{50\pi }=1/25\text{s}$


From the figure, we can see that, the time interval between value of current from zero $($at $t=0)$ to its first maximum value is $T/4$.

Therefore, time taken,

$t=\frac{1/25}{4}=1/100\text{s}=10\text{ms}$

Hence, $\left(\text{B}\right)$ is the correct answer.