In an $LCR$ series circuit,$R = 18 \ \Omega$ and the impedance $Z = 33 \ \Omega$. An $r.m.s.$ voltage of $V_{rms} = 220 \ V$ is applied across the circuit. The true power consumed in the $a.c.$ circuit is: (in $W$)

In a circuit,$L$,$C$,and $R$ are connected in series with an alternating voltage source of frequency $f$. When the current in the circuit leads the voltage by $45^{\circ}$,the value of $C$ is

In an $LCR$ series circuit, the potential difference across the terminals of the inductor, capacitor and resistor is $60 \text{ V}$, $30 \text{ V}$ and $40 \text{ V}$ respectively. Then the supply voltage will be equal to (in $\text{ V}$)

In the given $A.C.$ circuit,the instantaneous currents through the inductor and capacitor are $0.8 \,A$ and $0.4 \,A$ respectively. The instantaneous current through the resistor is:

Two coils require $20 \ min$ and $60 \ min$ respectively to produce the same amount of heat energy when connected separately to the same source. If they are connected in parallel to the same source,the time required to produce the same amount of heat by the combination of coils will be . . . . . . $min$.

In a series $RLC$ circuit,the $r.m.s.$ voltages across the resistor and the inductor are respectively $400 \,V$ and $700 \,V$. If the equation for the applied voltage is $\varepsilon = 500 \sqrt{2} \sin \omega t$,then the peak voltage across the capacitor is ........... $V$.