$A$ series $LCR$ circuit consists of $R = 80\,\Omega$,$X_{L} = 100\,\Omega$,and $X_{C} = 40\,\Omega$. The input voltage is $V = 2500 \cos(100\pi t)\,V$. The amplitude of current in the circuit is $................A$.

The power factor of an $RL$ circuit is $1/2$. If $R = 100 \, \Omega$,what is the value of $L$? The frequency of the $AC$ source is $50 \, Hz$.

$A$ resistor and a pure inductor are connected to an $AC$ supply of $120\,V$ and $50\,Hz$. The current in the circuit is $3\,A$. If the power consumed in the circuit is $108\,W$,then the resistance in the circuit is.....$\Omega $

In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is

In a series $CR$ circuit shown in the figure,the applied voltage is $10 \, V$ and the voltage across the capacitor is found to be $8 \, V$. Then the voltage across $R$,and the phase difference between the current and the applied voltage will respectively be:

For a series $LCR$ circuit,which one of the following is a $CORRECT$ statement?