(D) The power factor of an $LR$ circuit is given by $\cos \phi = R / Z$, where $Z = \sqrt{R^2 + X_L^2}$.For the initial $LR$ circuit, $X_L = 3R$, so $

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(D) The power factor of an $LR$ circuit is given by $\cos \phi = R / Z$, where $Z = \sqrt{R^2 + X_L^2}$.For the initial $LR$ circuit, $X_L = 3R$, so $Z_1 = \sqrt{R^2 + (3R)^2} = \sqrt{10R^2} = R\sqrt{10}$.Thus, $X_1 = R / (R\sqrt{10}) = 1 / \sqrt{10}$.After adding the capacitor in series, the circuit becomes an $LCR$ circuit with $X_{net} = X_L - X_C = 3R - R = 2R$.The new impedance is $Z_2 = \sqrt{R^2 + (2R)^2} = \sqrt{5R^2} = R\sqrt{5}$.Thus, $X_2 = R / (R\sqrt{5}) = 1 / \sqrt{5}$.The ratio $X_1 / X_2 = (1 / \sqrt{10}) / (1 / \sqrt{5}) = \sqrt{5} / \sqrt{10} = 1 / \sqrt{2}$.

Class 12 Physics Alternating Current RL, RC and LC AC Circuits

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An $a.c.$ source is applied to a series $LR$ circuit with $X_L = 3R$ and power factor is $X_1$. Now a capacitor with $X_c = R$ is added in series to the $LR$ circuit and the power factor is $X_2$. The ratio $X_1$ to $X_2$ is

MHT CET 2026 All MHT CET

A
$2 : 1$
B
$1 : 2$
C
$\sqrt{2} : 1$
D
$1 : \sqrt{2}$

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Class 12

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Alternating Current

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RL, RC and LC AC Circuits

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MHT CET 2026 Paper All MHT CET years →

Match List-$I$ with List-$II$:

List-$I$ List-$II$

$(a)$ Phase difference between current and voltage in a purely resistive $AC$ circuit $(i)$ $\frac{\pi}{2}$; current leads voltage

$(b)$ Phase difference between current and voltage in a pure inductive $AC$ circuit $(ii)$ zero

$(c)$ Phase difference between current and voltage in a pure capacitive $AC$ circuit $(iii)$ $\frac{\pi}{2}$; current lags voltage

$(d)$ Phase difference between current and voltage in an $LCR$ series circuit $(iv)$ $\tan^{-1}\left(\frac{X_C - X_L}{R}\right)$

Choose the most appropriate answer from the options given below:

List-$I$	List-$II$
$(a)$ Phase difference between current and voltage in a purely resistive $AC$ circuit	$(i)$ $\frac{\pi}{2}$; current leads voltage
$(b)$ Phase difference between current and voltage in a pure inductive $AC$ circuit	$(ii)$ zero
$(c)$ Phase difference between current and voltage in a pure capacitive $AC$ circuit	$(iii)$ $\frac{\pi}{2}$; current lags voltage
$(d)$ Phase difference between current and voltage in an $LCR$ series circuit	$(iv)$ $\tan^{-1}\left(\frac{X_C - X_L}{R}\right)$

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In an $L-R$ circuit,the value of $L$ is $(\frac{0.4}{\pi}) \, H$ and the value of $R$ is $30 \, \Omega$. If an alternating e.m.f. of $200 \, V$ at $50 \, Hz$ is connected to the circuit,what are the impedance and the current in the circuit?

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An $a.c.$ source is applied to a series $LR$ circuit with $X_L = 3R$ and power factor is $X_1$. Now a capacitor with $X_c = R$ is added in series to the $LR$ circuit and the power factor is $X_2$. The ratio $X_1$ to $X_2$ is

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In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is

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