Q140 / 150 · MHT CET 2025 (22 Apr Shift 2) · Physics

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 ? $\left(\mathrm{T}=\text { time period, } \sin 30^{\circ}=\frac{1}{2}\right)$

  • A
    $\frac{T}{8}$
  • B
    $\frac{\mathrm{T}}{4}$
  • Correct answer
    C
    $\frac{\mathrm{T}}{12}$
  • D
    $\frac{\mathrm{T}}{16}$

Solution

The alternating e.m.f. is characterized by $e = e_0 \sin \omega t$.

For $e = \frac{e_0}{2}$, solving $\sin \omega t = \frac{1}{2}$ yields $\omega t = \frac{\pi}{6}$.

Substituting $\omega = \frac{2\pi}{T}$ gives $\frac{2\pi}{T} t = \frac{\pi}{6}$, from which $t = \frac{T}{12}$.

The e.m.f. reaches half its maximum at $t = \frac{T}{12}$ from zero.

Hence, the correct answer is option: 'C'.

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