Question

At time t = 0 second, voltage of an A.C. Generator starts from 0V and becomes 2V at time $t=\frac{1}{100 \pi }$ second. The voltage keeps on increasing up 100V, after which it starts to decrease. Find the frequency of the Generator.

• A. $100 \, Hz$
• B. $1 \, Hz$
• C. $2 \, Hz$
• D. $5 \, Hz$

Answer 1

Answer: (B)

$\epsilon = \, \epsilon _{0}sin w t$
$\epsilon _{0}=maximum \, voltage=100V.$
at $t=\frac{1}{100 \pi }; \, \epsilon =100sin w\left(\frac{1}{100 \pi }\right)=2V$
$sin \frac{w}{100 \pi } = \frac{2}{100}$
$\frac{w}{100 \pi }=0.02 \, \, \, (for \,small \, \theta , sin\theta ≈\theta )$
$w=2\pi $
$f=\frac{w}{2 \pi }=1\,Hz$