Question

If an alternating voltage is given by the equation, $E=500\sin \left(100\pi t\right)\text{V}$, then calculate the time taken to reach from zero $($at $t=0)$ to its first maximum value.

• A. $1/10\text{s}$
• B. $1/200\text{s}$
• C. $1/50\text{s}$
• D. $1/20\text{s}$

Answer 1

The correct option is B $1/200\text{s}$

Given:

Voltage, $E=500\sin \left(100\pi t\right)\text{V}$

Comparing with $E=E_0\sin \omega t$, we get, angular frequency,

$\omega =100\pi \text{rad/s}$

So, time period, $T=\frac{2\pi }{\omega }=\frac{2\pi }{100\pi }=1/50\text{s}$


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

Therefore, time taken,

$t=\frac{1/50}{4}=1/200\text{s}$