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? (\(sin30^{\circ} = 0.5\))

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

Hint:

Set e0 sin(wt) equal to e0 divided by 2 and use w = 2 pi / T.

Answer 1

The Correct Option is C

Step 1: Use the angle.
One full period is $360^\circ$. The emf is half of the peak when the phase is $30^\circ$.

Step 2: Fraction of period.
$30/360 = 1/12$.

Step 3: Result.
The time is $T/12$.

Final Answer:
Option (C). \[ \boxed{\frac{T}{12}} \]