Question

The value of the A.C. voltage of a generator is V=O volts at time t= O. At time t=1/100π seconds, the voltage V=2 volts. The voltage keeps on increasing upto 100 volts. After that it starts decreasing. Determine the frequency of the voltage source. [Ans: 1 Hz]

Answer 1

The frequency of the voltage source is 1 Hz.

Given:

Time = $\bold{t=\frac{1}{100 \pi} \ s}$

Maximum produced voltage = $\bold{e_{o}=100 \ V}$

Voltage = e = 2 Volts

AC generator is used.

To find:

Frequency of the voltage source = ?

Solution:

The electric field in the AC generator is given by the formula:

$\bold{e=e_{o} \sin \omega t}$

On substituting the known values, we get,

$\bold{2=100 \sin \omega \times \frac{1}{100 \pi}}$

since, the given time is small. The angle in the above equation becomes,

$\bold{\sin \theta=\theta}$

$\bold{2=100 \times \omega \times \frac{1}{100 \pi}}$

$\bold{2 \pi=\omega}$

The formula of frequency is given as:

$\bold{2 \pi=2 \pi n}$

Where, n is frequency

Thus, n = 1 Hz