(A) Let $t^{\prime}$ be the time when the e.m.f. is half its maximum value.Given the equation $e = e_0 \sin \omega t$,we set $e = \frac{e_0}{2}$.$\fra

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(A) Let $t^{\prime}$ be the time when the e.m.f. is half its maximum value.Given the equation $e = e_0 \sin \omega t$,we set $e = \frac{e_0}{2}$.$\frac{e_0}{2} = e_0 \sin (\omega t^{\prime})$$\frac{1}{2} = \sin (\omega t^{\prime})$Since $\sin 30^{\circ} = 0.5$,we have $\omega t^{\prime} = \frac{\pi}{6}$.Substituting $\omega = \frac{2\pi}{T}$,we get:$(\frac{2\pi}{T}) t^{\prime} = \frac{\pi}{6}$$t^{\prime} = \frac{T}{12}$.

Class 12 Physics Alternating Current Alternating Current, Voltage (rms and Average)

Medium

An alternating e.m.f. is given as $e = e_0 \sin \omega t$. In what time will the e.m.f. have half its maximum value if $e$ starts from zero?
$(T = \text{time period}, \sin 30^{\circ} = \cos 60^{\circ} = 0.5)$

MHT CET 2022 All MHT CET

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

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An alternating e.m.f. is given as $e = e_0 \sin \omega t$. In what time will the e.m.f. have half its maximum value if $e$ starts from zero?$(T = \text{time period}, \sin 30^{\circ} = \cos 60^{\circ} = 0.5)$

Similar Questions

The variation of $EMF$ with time for four types of generators is shown in the figures. Which amongst them can be called $AC$?

$A$ group of lamps having a total power rating of $1000 \,W$ is supplied by an $AC$ voltage of $E = 200 \sin(310t + 60^{\circ})$. The $r.m.s.$ value of the current flowing through the circuit is:

Voltage and current in an $ac$ circuit are given by $V = 5\sin(100\pi t - \frac{\pi}{6})$ and $I = 4\sin(100\pi t + \frac{\pi}{6})$. Which of the following statements is correct?

Find the effective value of current $i = 2\sin(100\pi t) + 2\cos(100\pi t + 30^{\circ})$.

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An alternating e.m.f. is given as $e = e_0 \sin \omega t$. In what time will the e.m.f. have half its maximum value if $e$ starts from zero?
$(T = \text{time period}, \sin 30^{\circ} = \cos 60^{\circ} = 0.5)$