An $AC$ voltmeter connected between points $A$ and $B$ in the circuit below reads $36 \,V$. If it is connected between $A$ and $C$,the reading is $39 \,V$. The reading when it is connected between $B$ and $D$ is $25 \,V$. What is the reading when it is connected between $A$ and $D$? (Assume that the voltmeter reads true $rms$ voltage values and that the source generates a pure $AC$.)

$A$ $\frac{2.5}{\pi} \mu F$ capacitor and $3000 \, \Omega$ resistor are joined in series to an $AC$ source of $200 \, V$ and $50 \, Hz$ frequency. The power factor of the circuit and the power dissipated in it will respectively be:

When an inductor of inductance $L = \frac{6}{\pi} \ H$, a capacitor of capacitance $C = \frac{50}{\pi} \ \mu F$ and a resistor of resistance $R$ are connected in series with an $AC$ supply of rms voltage $V_{rms} = 220 \ V$ and frequency $f = 50 \ Hz$, the rms current through the circuit is $I_{rms} = 440 \ mA$. Match the inductive reactance $X_L$, the capacitive reactance $X_C$, the resistance $R$, and the impedance $Z$ of the circuit given in List-$I$ with the corresponding values given in List-$II$.

List-$I$	List-$II$
$(A) \ X_L$	$(i) \ 200 \ \Omega$
$(B) \ X_C$	$(ii) \ 300 \ \Omega$
$(C) \ R$	$(iii) \ 500 \ \Omega$
$(D) \ Z$	$(iv) \ 600 \ \Omega$

The reactance of a circuit is zero. It is possible that the circuit contains:

In the given circuit,the $AC$ source has $\omega = 100 \, rad \, s^{-1}$. Considering the inductor and capacitor to be ideal,what will be the current $I$ flowing through the circuit? (in $A$)

$A$ coil,a capacitor,and an $AC$ source of $rms$ voltage $24 \,V$ are connected in series. By varying the frequency of the source,a maximum $rms$ current of $6 \,A$ is observed. If the coil is connected to a battery of $emf$ $12 \,V$ and internal resistance $4 \,\Omega$,then the current through it in the steady state is......$A$