An inductor and a resistor are connected in series to an $AC$ source of voltage $V = 144 \sin \left(100 \pi t + \frac{\pi}{2}\right) \text{ V}$. If the current in the circuit is $I = 6 \sin \left(100 \pi t + \frac{\pi}{6}\right) \text{ A}$,then the resistance of the resistor is: (in $Omega$)

$A$ resistor and a capacitor are connected in series with an $AC$ source of angular frequency $\omega$. If the frequency is changed to $\omega / 3$ while keeping the voltage constant,the current becomes half. What is the ratio of the reactance to the resistance at the initial frequency?

In a series $LCR$ circuit,the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$,then the peak voltage across the inductor is

An $AC$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\omega/3$ (maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

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

The given figure represents the phasor diagram of a series $LCR$ circuit connected to an $ac$ source. At the instant $t'$ when the source voltage is given by $V = V_0 \cos(\omega t')$,the current in the circuit will be:
Given: $V_{OL} = 3 \text{ V}$,$V_{OR} = \sqrt{3} \text{ V}$,$V_{OC} = 2 \text{ V}$.