(D) In an $LCR$ series circuit, the phase difference $\phi$ is given by $\tan \phi = \frac{|X_L - X_C|}{R}$.When $L$ is removed, the circuit becomes a

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(D) In an $LCR$ series circuit, the phase difference $\phi$ is given by $\tan \phi = \frac{|X_L - X_C|}{R}$.When $L$ is removed, the circuit becomes an $RC$ circuit. The phase difference is $\tan(\pi/3) = \frac{X_C}{R} = \sqrt{3}$, so $X_C = R\sqrt{3}$.When $C$ is removed, the circuit becomes an $RL$ circuit. The phase difference is $\tan(\pi/3) = \frac{X_L}{R} = \sqrt{3}$, so $X_L = R\sqrt{3}$.Since $X_L = X_C$, the circuit is in resonance when all three components are connected.At resonance, the impedance $Z = R$, and the phase difference $\phi = 0$.The power factor is $\cos \phi = \cos(0) = 1$.

Class 12 Physics Alternating Current Mix Examples-Alternating Current

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$A$ resistor $R$, an inductor $L$, and a capacitor $C$ are connected in series with an a.c. source. When $L$ is removed from the circuit, the phase difference between voltage and current in the circuit is $\pi/3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi/3$. The power factor of the circuit is

MHT CET 2026 All MHT CET

A
$\sqrt{3}/2$
B
$1/2$
C
$1/\sqrt{2}$
D
$1$

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In an $LCR$ series circuit,when $L$ is removed from the circuit,the phase difference between voltage and current is $\frac{\pi}{3}$. If $C$ is removed from the circuit instead of $L$,the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $(\tan 60^{\circ}=\sqrt{3})$.

MediumMHT CET 2025

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In the shown $AC$ circuit,the phase difference between currents $I_1$ and $I_2$ is:

Medium

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An electrical device draws $2 \, kW$ power from $AC$ mains $(V_{rms} = 223 \, V = \sqrt{50000} \, V)$. The current lags in phase by $\tan \phi = -\frac{3}{4}$ compared to the voltage. Find $(i)$ $R$,$(ii)$ $X_C - X_L$,and $(iii)$ $I_M$. Another device has twice the values for $R$,$X_C$,and $X_L$. How are the answers affected?

Medium

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An $LCR$ series circuit with $100 \,\Omega$ resistance is connected to an $AC$ source of $200 \,V$ and angular frequency $300 \,rad/s$. When only the capacitance is removed,the current leads the voltage by $60^o$. When only the inductance is removed,the current lags the voltage by $60^o$. Then the current and power dissipated in the $LCR$ circuit are respectively:

Medium

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Given below are two statements:
Statement $I$: An $AC$ circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement $II$: An $AC$ circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of the above statements,choose the correct answer from the options given below:

MediumJEE MAIN 2023

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In an $LCR$ series circuit,when $L$ is removed from the circuit,the phase difference between voltage and current is $\frac{\pi}{3}$. If $C$ is removed from the circuit instead of $L$,the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $(\tan 60^{\circ}=\sqrt{3})$.

In the shown $AC$ circuit,the phase difference between currents $I_1$ and $I_2$ is:

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