Question

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In how much time the e.m.f. will have half its maximum value, if e starts from zero ? ($\text{T} = \text{Time Period, } \sin 30^\circ = \frac{1}{2}$)}

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

Hint:

$t = \frac{\theta}{360^\circ} T$. For $30^\circ$, $t = \frac{30}{360}T = \frac{T}{12}$.

Answer 1

The Correct Option is C

Step 1: Condition
$e = \frac{e_0}{2}$.
$e_0 \sin \omega t = \frac{e_0}{2} \implies \sin \omega t = \frac{1}{2}$.
Step 2: Solve for phase
$\omega t = 30^\circ = \frac{\pi}{6} \text{ radians}$.
Step 3: Time Calculation
Substitute $\omega = \frac{2\pi}{T}$:
$\frac{2\pi}{T} t = \frac{\pi}{6} \implies t = \frac{T}{12}$.
Final Answer: (C)