When a capacitor is connected in a series $LR$ circuit,what happens to the alternating current flowing in the circuit?

In a series $LR$ circuit,power of $400 \ W$ is dissipated from a source of $250 \ V, 50 \ Hz$. The power factor of the circuit is $0.8$. In order to bring the power factor to unity,a capacitor of value $C$ is added in series to the $L$ and $R$. Taking the value of $C$ as $(\frac{n}{3 \pi}) \mu F$,then the value of $n$ is $......$

In a series $L-C-R$ circuit,the inductive reactance is twice the resistance and the capacitive reactance is $1/3$ rd of the inductive reactance. The power factor of the circuit is

An $LCR$ series circuit with $R = 100\,\Omega$ is connected to a $200\,V, 50\,Hz$ $a.c.$ source. When only the capacitance is removed,the current lags the voltage by $60^o$. When only the inductance is removed,the current leads the voltage by $60^o$. The current in the circuit is.....$A$

An $LCR$ circuit contains resistance of $110 \, \Omega$ and a supply of $220 \, V$ at $300 \, rad/s$ angular frequency. If only capacitance is removed from the circuit,current lags behind the voltage by $45^{\circ}$. If on the other hand,only inductor is removed,the current leads by $45^{\circ}$ with the applied voltage. The rms current flowing in the circuit will be ...... $A$.

$A$ capacitor,an inductor,and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually,the electric bulb is found to