(B) The instantaneous voltage $V$ is given by $V = V_0 \sin(\omega t)$,where $V_0$ is the peak voltage and $\omega = 2\pi f$.Given $f = 50 \ Hz$,so $\

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(B) The instantaneous voltage $V$ is given by $V = V_0 \sin(\omega t)$,where $V_0$ is the peak voltage and $\omega = 2\pi f$.Given $f = 50 \ Hz$,so $\omega = 2 \times \pi \times 50 = 100\pi \ rad/s$.We want to find the time $t$ when $V = \frac{V_0}{2}$.Substituting this into the equation: $\frac{V_0}{2} = V_0 \sin(100\pi t)$.$\sin(100\pi t) = \frac{1}{2}$.Since $\sin(30^\circ) = \frac{1}{2}$,we have $100\pi t = \frac{\pi}{6}$.$t = \frac{\pi}{6 \times 100\pi} = \frac{1}{600} \ s$.

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

Medium

The frequency of an alternating voltage is $50 \ Hz$. The time taken for the instantaneous voltage to increase from zero to half of its peak voltage is:

TS EAMCET 2025 All TS EAMCET

A
$\frac{1}{800} \ s$
B
$\frac{1}{600} \ s$
C
$\frac{1}{300} \ s$
D
$\frac{1}{200} \ s$

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Alternating Current

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Alternating Current, Voltage (rms and Average)

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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?

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The voltage of an $ac$ supply varies with time $(t)$ as $V = 120\sin(100\pi t)\cos(100\pi t)$. The maximum voltage and frequency respectively are:

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An alternating current at any instant is given by $i = [6 + \sqrt{56} \sin (100 \pi t + \frac{\pi}{3})] \ A$. The rms value of the current is . . . . . . . (in $A$)

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$A$ generator produces a voltage that is given by $V = 240 \sin(120t)$,where $t$ is in seconds. The frequency and $r.m.s.$ voltage are:

Medium

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The variation of the instantaneous current $(I)$ and the instantaneous emf $(E)$ in a circuit is as shown in the figure. Which of the following statements is correct?

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The frequency of an alternating voltage is $50 \ Hz$. The time taken for the instantaneous voltage to increase from zero to half of its peak voltage is:

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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?

The voltage of an $ac$ supply varies with time $(t)$ as $V = 120\sin(100\pi t)\cos(100\pi t)$. The maximum voltage and frequency respectively are:

An alternating current at any instant is given by $i = [6 + \sqrt{56} \sin (100 \pi t + \frac{\pi}{3})] \ A$. The rms value of the current is . . . . . . . (in $A$)

$A$ generator produces a voltage that is given by $V = 240 \sin(120t)$,where $t$ is in seconds. The frequency and $r.m.s.$ voltage are:

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