(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 Questions

Class 12

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Chapter

Alternating Current

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RL, RC and LC AC Circuits

In an $RL$ circuit,the resistance is $\pi \sqrt{3} \,\Omega$. The phase difference between the current and the voltage is $30^\circ$. The $ac$ frequency is $50 \,Hz$. The inductance is . . . . . . $Henry$.

Easy

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In an $L-R$ circuit,the inductive reactance is equal to $\sqrt{3}$ times the resistance $R$ of the circuit. An e.m.f. $E = E_0 \sin(\omega t)$ is applied to the circuit. The power consumed in the circuit is:

MediumMHT CET 2025

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$A$ resistor of $450 \Omega$ and an inductor are connected in series to an ac source of frequency $\frac{75}{\pi} \text{ Hz}$. If the power factor of the circuit is $0.6$,then the inductance connected in the circuit is:

MediumAP EAMCET 2025

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The value of alternating emf $E$ in the given circuit will be......$V$.

Easy

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$A$ coil of negligible resistance is connected in series with a $90 \Omega$ resistor across a $120 \text{ V}, 60 \text{ Hz}$ supply. $A$ voltmeter reads $36 \text{ V}$ across the resistor. The inductance of the coil is: (in $\text{ H}$)

DifficultJEE MAIN 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 an $RL$ circuit,the resistance is $\pi \sqrt{3} \,\Omega$. The phase difference between the current and the voltage is $30^\circ$. The $ac$ frequency is $50 \,Hz$. The inductance is . . . . . . $Henry$.

In an $L-R$ circuit,the inductive reactance is equal to $\sqrt{3}$ times the resistance $R$ of the circuit. An e.m.f. $E = E_0 \sin(\omega t)$ is applied to the circuit. The power consumed in the circuit is:

$A$ resistor of $450 \Omega$ and an inductor are connected in series to an ac source of frequency $\frac{75}{\pi} \text{ Hz}$. If the power factor of the circuit is $0.6$,then the inductance connected in the circuit is:

The value of alternating emf $E$ in the given circuit will be......$V$.

$A$ coil of negligible resistance is connected in series with a $90 \Omega$ resistor across a $120 \text{ V}, 60 \text{ Hz}$ supply. $A$ voltmeter reads $36 \text{ V}$ across the resistor. The inductance of the coil is: (in $\text{ H}$)

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