Physics 2007 JAMB Past Questions - Question 20: The instantaneous value of the induced e.m.f. as a function of time is E=Eo sin wt Eo where £0 is the peak value of the e.m.f. The instantaneous value of the e.m.f., one quarter of the period, is

Correct Answer

A

Explanation

The instantaneous value of the induced electromotive force (e.m.f.) as a function of time is given by the equation:

E(t) = Eo * sin(ωt)

Where:
- E(t) is the e.m.f. at time 't'.
- Eo is the peak value of the e.m.f.
- ω is the angular frequency, which is equal to 2π times the frequency of the oscillation.

If you want to find the instantaneous e.m.f. at one-quarter of the period, you can calculate it by substituting t = T/4 into the equation, where T is the period of the oscillation:

E(T/4) = Eo * sin(ω * (T/4))

However, it's important to note that the value of sin(π/2) is 1, which occurs at t = T/4. Therefore, the instantaneous value of the e.m.f. at one-quarter of the period is:

E(T/4) = Eo * sin(π/2) = Eo * 1 = Eo

So, at one-quarter of the period, the e.m.f. is equal to the peak value Eo.