(D) The given voltage is $e = e_1 \sin \omega t + e_2 \cos \omega t$.We can rewrite this as $e = E_0 \sin(\omega t + \phi)$,where $E_0 = \sqrt{e_1^2 +

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$\sqrt{\frac{e_1^2 + e_2^2}{2}}$

(D) The given voltage is $e = e_1 \sin \omega t + e_2 \cos \omega t$.We can rewrite this as $e = E_0 \sin(\omega t + \phi)$,where $E_0 = \sqrt{e_1^2 + e_2^2}$ is the peak voltage.The root mean square $(RMS)$ value of an alternating voltage $e = E_0 \sin(\omega t + \phi)$ is given by $V_{rms} = \frac{E_0}{\sqrt{2}}$.Substituting the value of $E_0$,we get $V_{rms} = \frac{\sqrt{e_1^2 + e_2^2}}{\sqrt{2}} = \sqrt{\frac{e_1^2 + e_2^2}{2}}$.

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

Medium

An alternating voltage is given by: $e = e_1 \sin \omega t + e_2 \cos \omega t$. Then the root mean square $(RMS)$ value of the voltage is given by:

A
$\sqrt{e_1^2 + e_2^2}$
B
$\sqrt{e_1 e_2}$
C
$\sqrt{\frac{e_1 e_2}{2}}$
D
$\sqrt{\frac{e_1^2 + e_2^2}{2}}$

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Alternating Current

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Alternating Current, Voltage (rms and Average)

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 $A$)

DifficultJEE MAIN 2024

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If the instantaneous current is given by $i = 4 \cos(\omega t + \phi)$ amperes,then the $r.m.s.$ value of the current is:

Easy

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An $ac$ generator produces an output voltage $E = 170 \sin(377t) \text{ volts}$,where $t$ is in seconds. The frequency of the $ac$ voltage is......$Hz$.

Easy

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The instantaneous values of current and emf in an $AC$ circuit are $I = 1/\sqrt{2} \sin(314t) \, A$ and $E = \sqrt{2} \sin(314t - \pi/6) \, V$ respectively. The phase difference between $E$ and $I$ will be

Easy

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What is the approximate percentage value of the ratio of maximum voltage to its rms value in an $LCR$ $AC$ circuit (in $\%$)?

MediumGUJCET 2025

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An alternating voltage is given by: $e = e_1 \sin \omega t + e_2 \cos \omega t$. Then the root mean square $(RMS)$ value of the voltage is given by:

Similar Questions

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 $A$)

If the instantaneous current is given by $i = 4 \cos(\omega t + \phi)$ amperes,then the $r.m.s.$ value of the current is:

An $ac$ generator produces an output voltage $E = 170 \sin(377t) \text{ volts}$,where $t$ is in seconds. The frequency of the $ac$ voltage is......$Hz$.

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