In a radio receiver,the short wave and medium wave stations are tuned by using the same capacitor but coils of different inductance $L_s$ and $L_m$ respectively. Then:

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.....$W$

$A$ sinusoidal voltage of peak value $283 \;V$ and frequency $50 \;Hz$ is applied to a series $LCR$ circuit in which $R = 3 \;\Omega, L = 25.48 \;mH,$ and $C = 796 \;\mu F.$ Find
$(a)$ the impedance of the circuit;
$(b)$ the phase difference between the voltage across the source and the current;
$(c)$ the power dissipated in the circuit; and
$(d)$ the power factor.

In a series $R-L-C$ circuit,$R = 300 \, \Omega$,$L = 0.9 \, H$,$C = 2.0 \, \mu F$,and $\omega = 1000 \, rad/s$. The impedance of the circuit is ........ $\Omega$.

$A$ series $LCR$ circuit containing an $AC$ source of $100 \ V$ has an inductor and a capacitor of reactances $24 \ \Omega$ and $16 \ \Omega$ respectively. If a resistance of $6 \ \Omega$ is connected in series,then the potential difference across the series combination of inductor and capacitor only is (in $V$)

An inductance of $\frac{300}{\pi} \text{ mH}$,a capacitance of $\frac{1}{\pi} \text{ mF}$ and a resistance of $20 \ \Omega$ are connected in series with an a.c. source of $240 \text{ V}, 50 \text{ Hz}$. The phase angle of the circuit is