(D) In an $LR$ circuit,the phase angle $\phi$ between voltage and current is given by $\tan \phi = \frac{X_L}{R}$.Given $\phi = 45^{\circ}$,we have $\

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(D) In an $LR$ circuit,the phase angle $\phi$ between voltage and current is given by $\tan \phi = \frac{X_L}{R}$.Given $\phi = 45^{\circ}$,we have $\tan 45^{\circ} = 1$.Therefore,$\frac{X_L}{R} = 1$,which implies $X_L = R$.Given $R = 100 \ \Omega$,so $X_L = 100 \ \Omega$.The inductive reactance is $X_L = 2 \pi f L$.Substituting the values,$100 = 2 \pi \times 100 \times L$.Solving for $L$,we get $L = \frac{100}{2 \pi \times 100} = \frac{1}{2 \pi} \ H$.

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

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An inductance coil has a resistance of $100 \Omega$. When an $A.C.$ signal of frequency $100 \ Hz$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$

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A
$\frac{1}{\pi}$
B
$\frac{5}{2 \pi}$
C
$\frac{2}{\pi}$
D
$\frac{1}{2 \pi}$

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$A$ coil has $L = 0.04 \, H$ and $R = 12 \, \Omega$. When it is connected to a $220 \, V$,$50 \, Hz$ supply,the current flowing through the coil in amperes is: (in $.7$)

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An inductance coil has a resistance of $100 \Omega$. When an $A.C.$ signal of frequency $100 \ Hz$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$

Similar Questions

In the figure,if $A$ and $B$ are identical bulbs,which bulb glows brighter?

$A$ light bulb and an inductor coil are connected to an $AC$ source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb

An e.m.f. $E=E_0 \cos \omega t$ is applied to a circuit containing $L$ and $R$ in series. If $X_L=2 R$,then the power dissipated in the circuit is

In an $L-C-R$ series circuit,if $V$,$V_R$,$V_L$,and $V_C$ are the voltages across the source,resistor,inductor,and capacitor respectively at any instant,choose the correct relation.

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