In a series $L-C$ circuit,if $L=10^{-3} \,H$ and $C=3 \times 10^{-7} \,F$ is connected to a $100 \,V, 50 \,Hz$ a.c. source,the impedance of the circuit is ...........

In a series $R-C$ 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

$20\,V$ $AC$ is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is $12\,V$,the voltage across the coil is.....$V$.

$A$ series combination of resistor $R$ and capacitor $C$ is connected to an $A$.$C$. source of angular frequency $\omega$. Keeping the voltage same,if the frequency is changed to $\frac{\omega}{3}$,the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is

$A$ bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased,while keeping the voltage of the source constant,then

An e.m.f. $E = 4 \cos(1000t) \, V$ is applied to an $LR$-circuit of inductance $3 \, mH$ and resistance $4 \, \Omega$. The amplitude of current in the circuit is: