(C) Given: $X_L = R$ and $X_L = 2X_C$.From this, we get $X_C = X_L / 2 = R / 2$.The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^2

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(C) Given: $X_L = R$ and $X_L = 2X_C$.From this, we get $X_C = X_L / 2 = R / 2$.The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Substituting the values: $Z = \sqrt{R^2 + (R - R/2)^2} = \sqrt{R^2 + (R/2)^2} = \sqrt{R^2 + R^2/4} = \sqrt{5R^2/4} = \frac{\sqrt{5}R}{2}$.The phase difference $\phi$ is given by $\tan \phi = \frac{X_L - X_C}{R}$.Substituting the values: $\tan \phi = \frac{R - R/2}{R} = \frac{R/2}{R} = 1/2$.Therefore, $\phi = \tan^{-1}(1/2)$.

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

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For a series $LCR$ circuit, inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage $V$ and current $i$ are respectively

MHT CET 2026 All MHT CET

A
$\sqrt{5}R, \tan^{-1}(1/2)$
B
$\sqrt{5}R, \tan^{-1}(2)$
C
$\sqrt{5}R/2, \tan^{-1}(1/2)$
D
$\sqrt{5}R/2, \tan^{-1}(2)$

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Alternating Current

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RL, RC and LC AC Circuits

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$A$ resistance of $400\,\Omega$ is connected in series with an inductor of $(3/\pi)\,H$ and this combination is connected across an $A.C.$ source as shown in the figure,where $e = 400 \sin(100\pi t)$. Which of the following statements is correct?

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In an $AC$ circuit,a resistance of $R \, \Omega$ is connected in series with an inductance $L$. If the phase angle between voltage and current is $45^o$,the value of inductive reactance will be:

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An $AC$ circuit having supply voltage $E = 10 \sin \omega t$ consists of a resistor of resistance $R = 3 \Omega$ and an inductor of reactance $X_L = 4 \Omega$ as shown in the figure. The voltage across the inductor at $t = \pi / \omega$ is: (in $\text{ V}$)

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$A$ bulb and a capacitor are in series with an $ac$ source. On increasing the frequency,how will the glow of the bulb change?

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An inductance coil has a reactance of $100\, \Omega$. When an $AC$ signal of frequency $1000\, Hz$ is applied to the coil,the applied voltage leads the current by $45^{\circ}$. The self-inductance of the coil is

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For a series $LCR$ circuit, inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage $V$ and current $i$ are respectively

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$A$ resistance of $400\,\Omega$ is connected in series with an inductor of $(3/\pi)\,H$ and this combination is connected across an $A.C.$ source as shown in the figure,where $e = 400 \sin(100\pi t)$. Which of the following statements is correct?

In an $AC$ circuit,a resistance of $R \, \Omega$ is connected in series with an inductance $L$. If the phase angle between voltage and current is $45^o$,the value of inductive reactance will be:

An $AC$ circuit having supply voltage $E = 10 \sin \omega t$ consists of a resistor of resistance $R = 3 \Omega$ and an inductor of reactance $X_L = 4 \Omega$ as shown in the figure. The voltage across the inductor at $t = \pi / \omega$ is: (in $\text{ V}$)

$A$ bulb and a capacitor are in series with an $ac$ source. On increasing the frequency,how will the glow of the bulb change?

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