For the $L-R$ circuit shown in the figure,calculate the phase angle in degrees if the frequency is $f = 100/\pi \ Hz$. The inductance is $L = 0.025 \ H$ and the resistance is $R = 5 \ \Omega$.

An induction coil has an impedance of $10\,\Omega$. When an $AC$ signal of frequency $1000\,Hz$ is applied to the coil,the voltage leads the current by $45^o$. The inductance of the coil is

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

$A$ series $L, R$ circuit connected with an ac source $E = (25 \sin 1000 t) \ V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E = (20 \sin 2000 t) \ V$,the new power factor of the circuit will be:

An $ac$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\omega/3$ (while maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

An e.m.f. $E = E_0 \cos \omega t$ is applied to an $L-R$ circuit. The inductive reactance is equal to the resistance $R$ of the circuit. The power consumed in the circuit is: