Question

An alternating e.m.f. is given by \(e = e_0sinωt\). In what time the e.m.f. will have half its maximum value, if 'e' Starts from zero?

• A. \(\frac{\text{T}}{4}\)
• B. \(\frac{\text{T}}{8}\)
• C. \(\frac{\text{T}}{12}\)
• D. \(\frac{\text{T}}{16}\)

Hint:

Set sin(wt) = 1/2 and use w = 2 pi / T.

Answer 1

The Correct Option is C

Step 1: Use degrees of phase:
A full period is $360^\circ$. $\sin\theta = \tfrac12$ at $\theta = 30^\circ$.

Step 2: Fraction of the period:
$30^\circ/360^\circ = \tfrac1{12}$.

Step 3: Time:
$t = T/12$, option (C).

Final Answer:
The time is T / 12. \[ \boxed{\text{(C) }\dfrac{T}{12}} \]