(B) The impedance of an $LCR$ series circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.At resonance,the inductive reactance $X_L$ is equal to the c

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at resonance,impedance of the circuit is $12 \text{ } \Omega$.

(B) The impedance of an $LCR$ series circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.At resonance,the inductive reactance $X_L$ is equal to the capacitive reactance $X_C$,i.e.,$X_L = X_C$.Substituting this into the impedance formula:$Z = \sqrt{R^2 + (0)^2} = R$.Given $R = 12 \text{ } \Omega$,the impedance at resonance is $Z = 12 \text{ } \Omega$.

Class 12 Physics Alternating Current Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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$L=2 \text{ H}, C=5 \text{ mF}$ and $R=12 \text{ } \Omega$ are connected in series to an a.c. generator of frequency $50 \text{ Hz}$. Then:

MHT CET 2024 All MHT CET

A
at resonance,impedance of the circuit is zero.
B
at resonance,impedance of the circuit is $12 \text{ } \Omega$.
C
the resonant frequency of the circuit is $1 / 2 \pi \text{ Hz}$.
D
the inductive reactance is less than the capacitive reactance.

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Alternating Current

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad/s$. At resonance,the voltage across $L$ is......$V$.

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Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

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In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

Medium

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In a series $LR$ circuit with $X_L = R$, the power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C = X_L$ is added to the circuit, the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be:

MediumJEE MAIN 2023

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With a gradual increase in the frequency of an $A.C.$ supply,the impedance of an $LCR$ series circuit

EasyMHT CET 2024

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$L=2 \text{ H}, C=5 \text{ mF}$ and $R=12 \text{ } \Omega$ are connected in series to an a.c. generator of frequency $50 \text{ Hz}$. Then:

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In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad/s$. At resonance,the voltage across $L$ is......$V$.

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

In a series $LR$ circuit with $X_L = R$, the power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C = X_L$ is added to the circuit, the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be:

With a gradual increase in the frequency of an $A.C.$ supply,the impedance of an $LCR$ series circuit

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