$A$ series $R-L-C$ circuit consists of an $8.0\ \Omega$ resistor,a $5.0\ \mu F$ capacitor,and a $50.0\ mH$ inductor. $A$ variable frequency source applies an $emf$ of $400\ V\ (rms)$ across the combination. The power delivered to the circuit when the frequency is equal to one-half the resonance frequency is.....$W$

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 ...... $A$.

The figure shows a combination of inductances and capacitances. The resonant frequency of the $L-C$ circuit is:

In a series $LCR$ circuit,$R$ represents the resistance of an electric bulb. If the frequency of the $A.C.$ supply is doubled,what should be the values of inductance $L$ and capacitance $C$ to maintain the same current?

$A$ sinusoidal voltage of peak value $283 \;V$ and frequency $50 \;Hz$ is applied to a series $LCR$ circuit in which $R = 3 \;\Omega, L = 25.48 \;mH,$ and $C = 796 \;\mu F.$ Find
$(a)$ the impedance of the circuit;
$(b)$ the phase difference between the voltage across the source and the current;
$(c)$ the power dissipated in the circuit; and
$(d)$ the power factor.

$A$ circuit has a resistance of $11\,\Omega$,an inductive reactance of $25\,\Omega$,and a capacitive reactance of $18\,\Omega$. It is connected to an $AC$ source of $260\,V$ and $50\,Hz$. The current through the circuit (in amperes) is: