(A) For $d.c.$ supply,the inductor acts as a pure resistor:$R = \frac{V}{I} = \frac{100 \ V}{1 \ A} = 100 \ \Omega$.For $a.c.$ supply,the impedance $Z

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$200 \ \Omega, \frac{\sqrt{3}}{\pi} \ H$

(A) For $d.c.$ supply,the inductor acts as a pure resistor:$R = \frac{V}{I} = \frac{100 \ V}{1 \ A} = 100 \ \Omega$.For $a.c.$ supply,the impedance $Z$ is given by:$Z = \frac{V}{I} = \frac{100 \ V}{0.5 \ A} = 200 \ \Omega$.The impedance of an $LR$ circuit is $Z = \sqrt{R^2 + X_L^2}$,where $X_L = 2 \pi f L$.Substituting the values: $200 = \sqrt{100^2 + X_L^2}$.Squaring both sides: $40000 = 10000 + X_L^2 \Rightarrow X_L^2 = 30000$.$X_L = \sqrt{30000} = 100\sqrt{3} \ \Omega$.Since $X_L = 2 \pi f L$,we have $100\sqrt{3} = 2 \pi (50) L$.$100\sqrt{3} = 100 \pi L \Rightarrow L = \frac{\sqrt{3}}{\pi} \ H$.

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

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When $100 \ V$ $d.c.$ is applied across a solenoid,a current of $1 \ A$ flows in it. When $100 \ V$ $a.c.$ is applied across it,the current drops to $0.5 \ A$. If the frequency is $50 \ Hz$,the impedance and inductance are:

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$200 \ \Omega, \frac{\sqrt{3}}{\pi} \ H$
B
$100 \ \Omega, \sqrt{3} \ H$
C
$200 \ \Omega, 1 \ H$
D
$100 \ \Omega, 1 \ H$

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An inductor of self-inductance $1 \ H$ is connected in series with a resistor of $100 \pi \ \Omega$ and an $AC$ supply of $100 \pi \ V$,$50 \ Hz$. The maximum current flowing in the circuit is . . . . . . $A$.

MediumJEE MAIN 2025

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When an $AC$ source of emf $E$ with angular frequency $\omega = 100 \text{ rad/s}$ is connected across a circuit, the phase difference between $E$ and current $I$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consists of only $RC$ or $RL$ in series, then:

EasyWBJEE 2022

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When $100 \, V$ $DC$ is applied across a coil,a current of $1 \, A$ flows through it. When $100 \, V$ $AC$ at $50 \, Hz$ is applied to the same coil,only $0.5 \, A$ current flows. The impedance of the coil is ....... $\Omega$.

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An ideal choke draws a current of $8 \, A$ when connected to an $AC$ supply of $100 \, V, 50 \, Hz$. $A$ pure resistor draws a current of $10 \, A$ when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the $AC$ source of $150 \, V, 40 \, Hz$. The current in the circuit becomes

DifficultKCET 2010

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An inductive circuit contains a resistance of $10 \, \Omega$ and an inductance of $2.0 \, H$. If an $AC$ voltage of $120 \, V$ and frequency $60 \, Hz$ is applied to this circuit,the current would be nearly: ..... $A$

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When $100 \ V$ $d.c.$ is applied across a solenoid,a current of $1 \ A$ flows in it. When $100 \ V$ $a.c.$ is applied across it,the current drops to $0.5 \ A$. If the frequency is $50 \ Hz$,the impedance and inductance are:

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An inductor of self-inductance $1 \ H$ is connected in series with a resistor of $100 \pi \ \Omega$ and an $AC$ supply of $100 \pi \ V$,$50 \ Hz$. The maximum current flowing in the circuit is . . . . . . $A$.

When an $AC$ source of emf $E$ with angular frequency $\omega = 100 \text{ rad/s}$ is connected across a circuit, the phase difference between $E$ and current $I$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consists of only $RC$ or $RL$ in series, then:

When $100 \, V$ $DC$ is applied across a coil,a current of $1 \, A$ flows through it. When $100 \, V$ $AC$ at $50 \, Hz$ is applied to the same coil,only $0.5 \, A$ current flows. The impedance of the coil is ....... $\Omega$.

An inductive circuit contains a resistance of $10 \, \Omega$ and an inductance of $2.0 \, H$. If an $AC$ voltage of $120 \, V$ and frequency $60 \, Hz$ is applied to this circuit,the current would be nearly: ..... $A$

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