(B) The power factor of an $LCR$ circuit is given by $\cos \phi = \frac{R}{Z}$,where $R$ is the resistance and $Z$ is the impedance of the circuit.Giv

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(B) The power factor of an $LCR$ circuit is given by $\cos \phi = \frac{R}{Z}$,where $R$ is the resistance and $Z$ is the impedance of the circuit.Given:Resistance $R = 80 \ \Omega$Inductive reactance $X_L = 70 \ \Omega$Capacitive reactance $X_C = 130 \ \Omega$The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Substituting the values:$Z = \sqrt{80^2 + (70 - 130)^2}$$Z = \sqrt{80^2 + (-60)^2}$$Z = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \ \Omega$.Now,the power factor $x = \cos \phi = \frac{R}{Z} = \frac{80}{100} = 0.8$.

Class 12 Physics Alternating Current Power in AC and Power Factor

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$A$ series $LCR$ circuit is connected to an a.c. source of $230 \ V, 50 \ Hz$. The circuit contains a resistance of $80 \ \Omega$,an inductor having inductive reactance $70 \ \Omega$,and a capacitor of capacitive reactance $130 \ \Omega$. The power factor of the circuit is $x$. The value of $x$ is

MHT CET 2025 All MHT CET

A
$0.4$
B
$0.8$
C
$0.6$
D
$0.9$

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Class 12

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Chapter

Alternating Current

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Power in AC and Power Factor

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In an $A.C.$ circuit,the instantaneous values of $\text{e.m.f}.$ and current are $e = 10 \sin(50 \pi t) \text{ V}$ and $I = 10 \sin(50 \pi t + \frac{\pi}{3}) \text{ A}$. The average power consumed in the circuit is $... \text{ W}$.

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In an $A.C.$ circuit containing $L$, $C$ and $R$ in series, the ratio of apparent power to the true power is ($Z=$ impedance of the circuit and $R=$ resistance).

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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:

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$A$ series $LCR$ circuit is connected to an a.c. source of $230 \ V, 50 \ Hz$. The circuit contains a resistance of $80 \ \Omega$,an inductor having inductive reactance $70 \ \Omega$,and a capacitor of capacitive reactance $130 \ \Omega$. The power factor of the circuit is $x$. The value of $x$ is

Similar Questions

The power dissipated in a resistor of resistance $R$ when an alternating current with a peak value of $I_p$ flows through it is:

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......$W$

In an $A.C.$ circuit,the instantaneous values of $\text{e.m.f}.$ and current are $e = 10 \sin(50 \pi t) \text{ V}$ and $I = 10 \sin(50 \pi t + \frac{\pi}{3}) \text{ A}$. The average power consumed in the circuit is $... \text{ W}$.

In an $A.C.$ circuit containing $L$, $C$ and $R$ in series, the ratio of apparent power to the true power is ($Z=$ impedance of the circuit and $R=$ resistance).

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:

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