Ac Voltage

The given equation for the alternating voltage is: where represents the amplitude of the voltage, and is the angular frequency ( ).
(i) Peak value of e.m.f.
The peak value of an alternating voltage is the maximum voltage that the wave attains. By inspecting the equation, it is clear that the peak value of the e.m.f. corresponds to the amplitude of the sine function.
Therefore:

(ii) Frequency of e.m.f.

The angular frequency is related to the frequency by the equation:

Given that , we can solve for :

Thus, the frequency of the e.m.f. is .

(iii) Instantaneous value of e.m.f. at

To find the instantaneous value of the e.m.f. at time , we substitute into the equation:

Now, is very close to , and we know that:

Thus:

So the instantaneous value of the e.m.f. at is:

Therefore, the instantaneous value of the e.m.f. at is .