In which of the following $AC$ circuit, we get the value of power factor $1$ at resonance condition?

$A$ series $LCR$ circuit with $R=20\; \Omega, L=1.5\; H$ and $C=35\; \mu F$ is connected to a variable-frequency $200\; V$ $ac$ supply. When the frequency of the supply equals the natural frequency of the circuit,what is the average power (in $W$) transferred to the circuit in one complete cycle?

In an $LRC$ series circuit at resonance,the current in the circuit is $10\sqrt{2} \ A$. If the frequency of the source is changed such that the current now lags by $45^o$ behind the applied voltage,which of the following is correct?

Obtain the equation of bandwidth for an $L-C-R$ series $AC$ circuit and deduce the equation of $Q$ factor.

In an $L-C-R$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to:

In a series $LR$ circuit with $X_L = R$, 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: