$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be

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:

When $100 \ V$ $d.c.$ is applied across a solenoid,a current of $1 \ A$ flows in it. When $100 \ V$ $a.c.$ is applied across it,the current drops to $0.5 \ A$. If the frequency is $50 \ Hz$,the impedance and inductance are:

$A$ resistor of $500 \Omega$ and an inductor of $0.5 \ H$ are connected in series with an $AC$ source given by $V = 100 \sqrt{2} \sin(1000 t)$. The power factor of the combination is:

An alternating emf is applied across a parallel combination of a resistance $R$,capacitance $C$ and an inductance $L$. If $I_R$,$I_L$,and $I_C$ are the currents through $R$,$L$,and $C$ respectively,then the diagram which correctly represents the phase relationship among $I_R$,$I_L$,$I_C$,and the source emf $E$ is:

For the series $LCR$ circuit,$R = \frac{X_L}{2} = 2 X_C$. The impedance of the circuit and the phase difference between $V$ and $I$ will be