$A$ circuit when connected to an $A.C.$ source of $12 \; V$ gives a current of $0.2 \; A$. The same circuit when connected to a $D.C.$ source of $12 \; V$,gives a current of $0.4 \; A$. The circuit is

In an $LCR$ series circuit,an inductor $30 \, {mH}$ and a resistor $1 \, \Omega$ are connected to an $AC$ source of angular frequency $300 \, {rad/s}$. The value of capacitance for which the current leads the voltage by $45^{\circ}$ is $\frac{1}{x} \times 10^{-3} \, {F}$. Then the value of $x$ is ..... .

If $i$ is the current in an $L-C-R$ series $AC$ circuit,what are the formulas for:
$(i)$ Voltage across resistance.
$(ii)$ Voltage across inductor.
$(iii)$ Voltage across capacitor.

$A$ circuit connected to an $ac$ source of $emf$ $e = e_0 \sin(1000t)$,where $t$ is in seconds,exhibits a phase difference of $\frac{\pi}{4}$ between the $emf$ $e$ and current $i$. Which of the following circuits will exhibit this?

An $ac$ voltage is applied to a resistance $R$ and an inductor $L$ in series. If $R$ and the inductive reactance are both equal to $3\,\Omega$,the phase difference between the applied voltage and the current in the circuit is

To light a $50\,W, 100\,V$ lamp,it is connected in series with a capacitor of capacitance $C = \frac{50}{\pi \sqrt{x}} \mu F$ to a $200\,V, 50\,Hz$ $AC$ source. The value of $x$ is........