In a series $LCR$ circuit, $R = 10 \ \Omega$ and the impedance $Z = 30 \ \Omega$. An $r.m.s.$ voltage of $210 \text{ V}$ is applied across the circuit. The true power consumed in the $AC$ circuit is: (in $\text{ W}$)

When a capacitor is connected in series with an $LR$ circuit, the alternating current flowing in the circuit:

$A$ circuit containing an $80 \; mH$ inductor,a resistance of $15 \; \Omega$,and a $60 \; \mu F$ capacitor in series is connected to a $230 \; V, 50 \; Hz$ supply. Obtain the average power transferred to each element of the circuit,and the total power absorbed.

As given in the figure,a series circuit connected across a $200\, V$,$60\, Hz$ line consists of a capacitor of capacitive reactance $30\,\Omega$,a non-inductive resistor of $44\,\Omega$,and a coil of inductive reactance $90\,\Omega$ and resistance $36\,\Omega$. The power dissipated in the coil is......$W$

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:

Obtain the relation for the voltage applied to a series $LCR$ circuit.