The adjoining figure shows an $AC$ circuit with resistance $R$,inductance $L$ and source voltage $V_s$. Then

An $AC$ voltage $V = 5 \cos(1000t) \text{ V}$ is applied to an $L-R$ circuit of inductance $3 \text{ mH}$ and resistance $4 \text{ } \Omega$. The value of maximum current in the circuit is . . . . . . $A$.

$A$ light bulb connected in series with a capacitor and an $a.c.$ source is glowing with certain brightness. On reducing the value of capacitance and frequency respectively, the brightness of the bulb

$A$ $20 V$ $AC$ is applied to a circuit consisting of a resistor and a coil with negligible resistance. If the voltage across the resistor is $12 V$,the voltage across the coil is (in $V$)

When a $DC$ voltage of $200\, V$ is applied to a coil of self-inductance $\frac{2\sqrt{3}}{\pi}\,H$,a current of $1\, A$ flows through it. When the $DC$ source is replaced by an $AC$ source of $200\, V$,the current in the coil is reduced to $0.5\, A$. The frequency of the $AC$ supply is......$Hz$.

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 $\omega/3$ (while 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 $\omega$.