(C) The average power $P$ in an $AC$ circuit is given by the formula:$P = V_{rms} I_{rms} \cos \phi$Since $V_{rms} = I_{rms} Z$ and the power factor $

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(C) The average power $P$ in an $AC$ circuit is given by the formula:$P = V_{rms} I_{rms} \cos \phi$Since $V_{rms} = I_{rms} Z$ and the power factor $\cos \phi = \frac{R}{Z}$,where $Z$ is the impedance of the circuit and $R$ is the resistance.Substituting these into the power formula:$P = (I_{rms} Z) \times I_{rms} \times \left( \frac{R}{Z} \right)$$P = I_{rms}^2 R$Given that $I_{rms} = 2 A$ and $R = 5 \Omega$:$P = (2)^2 \times 5$$P = 4 \times 5 = 20 \, W$Therefore,the average power in the circuit is $20 \, W$.

Class 12 Physics Alternating Current Power in AC and Power Factor

Medium

$A$ capacitor $C = 2 \mu F$ and an inductor with $L = 10 H$ and coil resistance $R = 5 \Omega$ are connected in series in a circuit. When an alternating current of $r.m.s.$ value $I_{rms} = 2 A$ flows in the circuit,the average power in watts in the circuit is:

A
$100$
B
$50$
C
$20$
D
$10$

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Alternating Current

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Power in AC and Power Factor

The potential difference $V$ and the current $I$ flowing through an instrument in an $AC$ circuit of frequency $f$ are given by $V = 5 \cos(\omega t)$ volts and $I = 2 \sin(\omega t)$ amperes (where $\omega = 2 \pi f$). The power dissipated in the instrument is......$W$

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The impedance of a circuit consists of $3 \, \Omega$ resistance and $4 \, \Omega$ reactance. The power factor of the circuit is

Medium

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The potential differences across the resistance,capacitance,and inductance are $80 \, V$,$40 \, V$,and $100 \, V$ respectively in an $L-C-R$ circuit. The power factor of this circuit is:

MediumNEET 2016

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The instantaneous values of alternating current and voltage in a circuit are given as $I = \frac{1}{\sqrt{2}} \sin(100\pi t)$ and $E = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3})$. The average power in watts consumed in the circuit is:

MediumAIPMT 2012

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In an $ac$ circuit,the current is given by $i = 5 \sin \left( 100 t - \frac{\pi}{2} \right)$ and the $ac$ potential is $V = 200 \sin (100 t) \text{ volts}$. Then the power consumption is $....... \text{ watts}$.

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$A$ capacitor $C = 2 \mu F$ and an inductor with $L = 10 H$ and coil resistance $R = 5 \Omega$ are connected in series in a circuit. When an alternating current of $r.m.s.$ value $I_{rms} = 2 A$ flows in the circuit,the average power in watts in the circuit is:

Similar Questions

The potential difference $V$ and the current $I$ flowing through an instrument in an $AC$ circuit of frequency $f$ are given by $V = 5 \cos(\omega t)$ volts and $I = 2 \sin(\omega t)$ amperes (where $\omega = 2 \pi f$). The power dissipated in the instrument is......$W$

The impedance of a circuit consists of $3 \, \Omega$ resistance and $4 \, \Omega$ reactance. The power factor of the circuit is

The potential differences across the resistance,capacitance,and inductance are $80 \, V$,$40 \, V$,and $100 \, V$ respectively in an $L-C-R$ circuit. The power factor of this circuit is:

The instantaneous values of alternating current and voltage in a circuit are given as $I = \frac{1}{\sqrt{2}} \sin(100\pi t)$ and $E = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3})$. The average power in watts consumed in the circuit is:

In an $ac$ circuit,the current is given by $i = 5 \sin \left( 100 t - \frac{\pi}{2} \right)$ and the $ac$ potential is $V = 200 \sin (100 t) \text{ volts}$. Then the power consumption is $....... \text{ watts}$.

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