With an increase in the frequency of an $a.c.$ supply,the impedance of an $LCR$ series circuit:

An $LCR$ series circuit with a resistance of $100 \, \Omega$ is connected to an $ac$ source of $200 \, V \, (r.m.s.)$ and angular frequency $300 \, rad/s$. When only the capacitor is removed, the current lags behind the voltage by $60^o$. When only the inductor is removed, the current leads the voltage by $60^o$. The average power dissipated is.....$W$

In an $LCR$ series circuit,if the angular frequency $\omega$ is gradually increased,then match the following columns:

Column-$I$	Column-$II$
$(A)$ Capacitive reactance	$(i)$ Will continuously increase
$(B)$ Inductive reactance	(ii) Will remain constant
$(C)$ Resistance	(iii) Will first decrease and then increase
$(D)$ Total impedance	(iv) Will continuously decrease

An inductor of reactance $100 \ \Omega$, a capacitor of reactance $50 \ \Omega$, and a resistor of resistance $50 \ \Omega$ are connected in series with an $AC$ source of $10 \ V, 50 \ Hz$. Average power dissipated by the circuit is . . . . . . $W$.

The power factor of the given $LCR$ circuit is $1/\sqrt{2}$. Find the capacitance $C$ of the circuit in $\mu F$.

An inductor $20 \, mH$,a capacitor $50 \, \mu F$ and a resistor $40 \, \Omega$ are connected in series across a source of emf $V = 10 \, \sin \, 340t$. The power loss in the $A.C.$ circuit is ...... $W$.