In a series $LCR$ circuit,the voltage across the resistance,capacitance,and inductance is $10 \, V$ each. If the inductor is short-circuited,what will be the voltage across the capacitor?

$A$ coil has an inductance of $10 \, mH$. When it is connected to a $10 \, V \, dc$ source,the power dissipation is $20 \, W$. When it is connected to a $10 \, V \, ac$ source,the power dissipation is $10 \, W$. What is the frequency of the $ac$ source in $Hz$?

An $AC$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current flowing in the circuit is found to be $I$. Now,the frequency of the source is changed to $\frac{\omega}{3}$ (maintaining the same voltage),and the current in the circuit is found to be halved. What is the ratio of reactance to resistance at the original frequency?

An $AC$ voltage $V = 5 \cos(1000t) \text{ V}$ is applied to an $L-R$ circuit of inductance $3 \text{ mH}$ and resistance $4 \text{ } \Omega$. The value of maximum current in the circuit is . . . . . . $A$.

When a d.c. voltage of $200 \, V$ is applied to a coil of self-inductance $\left(\frac{2 \sqrt{3}}{\pi}\right) \, H$, a current of $1 \, A$ flows through it. But by replacing the d.c. source with an a.c. source of $200 \, V$, the current in the coil is reduced to $0.5 \, A$. Then the frequency of the a.c. supply is: (in $ \, Hz$)

An $A.C.$ circuit contains a resistance of $12 \ \Omega$ and an inductive reactance of $5 \ \Omega$. The phase angle between the current and the potential difference will be