An inductance of $0.2 \ H$ and resistance of $100 \ \Omega$ are connected in series to an $AC$ of $180 \ V$,$50 \ Hz$ supply. The $RMS$ current flowing in the circuit will be . . . . . . (Take $\pi^2$ as $10$). (in $A$)

When $80 \ V$ $d.c.$ is applied across a solenoid,a current of $0.8 \ A$ flows in it. When $80 \ V$ $a.c.$ is applied across the same solenoid,the current becomes $0.4 \ A$. If the frequency of $a.c.$ source is $50 \ Hz$,the impedance and inductance of the solenoid are nearly:

In an $AC$ circuit,the potential differences across an inductance and a resistance joined in series are $16 \, V$ and $20 \, V$ respectively. The total potential difference of the source is .......... $V$.

In a series $LR$ circuit,$X_L=R$,the power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C=X_L$ is added to the circuit,the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be

In an $L-R$ circuit,the inductive reactance is equal to the resistance $R$ in the circuit. An emf $E = E_0 \cos \omega t$ is applied to the circuit. The power consumed 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.