(D) The phase difference $\phi$ in an $LR$ series circuit is given by $\tan \phi = \frac{X_L}{R}$.Here,$X_L = 2\pi \nu L$,where $\nu = 50 \, Hz$ and $

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(D) The phase difference $\phi$ in an $LR$ series circuit is given by $\tan \phi = \frac{X_L}{R}$.Here,$X_L = 2\pi \nu L$,where $\nu = 50 \, Hz$ and $R = \pi \sqrt{3} \, \Omega$.Given $\phi = 30^o$,we have $\tan 30^o = \frac{2\pi \times 50 \times L}{\pi \sqrt{3}}$.Since $\tan 30^o = \frac{1}{\sqrt{3}}$,the equation becomes $\frac{1}{\sqrt{3}} = \frac{100\pi L}{\pi \sqrt{3}}$.Canceling $\sqrt{3}$ from both denominators,we get $1 = 100L$.Therefore,$L = \frac{1}{100} = 0.01 \, H$.

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

Easy

What will be the self-inductance of a coil,to be connected in series with a resistance of $\pi \sqrt{3} \, \Omega$,such that the phase difference between the $EMF$ and the current at $50 \, Hz$ frequency is $30^o$ (in $, H$)?

A
$0.5$
B
$0.03$
C
$0.05$
D
$0.01$

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Class 12

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Alternating Current

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RL, RC and LC AC Circuits

In the given circuit,the angular frequency of the voltage source is $70 \times 10^3 \text{ rad s}^{-1}$. The circuit effectively behaves like,

EasyAP EAMCET 2019

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An $A.C.$ source is connected to a series $LCR$ circuit. If the voltage across $R$ is $40 \,V$, the voltage across $L$ is $80 \,V$, and the voltage across $C$ is $40 \,V$, then the e.m.f. '$e$' of the $A.C.$ source is:

DifficultMHT CET 2023

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There is a $5\,\Omega$ resistance in an $AC$ circuit. An inductance of $0.1\,H$ is connected in series with it. If the equation of the $AC$ $EMF$ is $E = 5\sin(50t)$,then the phase difference between the current and the $EMF$ is:

Medium

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Which one of the following curves represents the variation of impedance $(Z)$ with frequency $(f)$ in a series $L-C-R$ circuit,when connected to an $AC$ source?

EasyTS EAMCET 2020

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An inductor of inductive reactance $R$,a capacitor of capacitive reactance $2R$,and a resistor of resistance $R$ are connected in series to an $AC$ source. The power factor of the series $LCR$ circuit is

EasyTS EAMCET 2024

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What will be the self-inductance of a coil,to be connected in series with a resistance of $\pi \sqrt{3} \, \Omega$,such that the phase difference between the $EMF$ and the current at $50 \, Hz$ frequency is $30^o$ (in $, H$)?

Similar Questions

In the given circuit,the angular frequency of the voltage source is $70 \times 10^3 \text{ rad s}^{-1}$. The circuit effectively behaves like,

An $A.C.$ source is connected to a series $LCR$ circuit. If the voltage across $R$ is $40 \,V$, the voltage across $L$ is $80 \,V$, and the voltage across $C$ is $40 \,V$, then the e.m.f. '$e$' of the $A.C.$ source is:

There is a $5\,\Omega$ resistance in an $AC$ circuit. An inductance of $0.1\,H$ is connected in series with it. If the equation of the $AC$ $EMF$ is $E = 5\sin(50t)$,then the phase difference between the current and the $EMF$ is:

Which one of the following curves represents the variation of impedance $(Z)$ with frequency $(f)$ in a series $L-C-R$ circuit,when connected to an $AC$ source?

An inductor of inductive reactance $R$,a capacitor of capacitive reactance $2R$,and a resistor of resistance $R$ are connected in series to an $AC$ source. The power factor of the series $LCR$ circuit is

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