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 . . . . . . $W$.

$A$ capacitor and an inductance coil are connected in separate $AC$ circuits with a bulb glowing in both the circuits. The bulb glows more brightly when

In an $LCR$ circuit,$R = 100 \ \Omega$. When the capacitor $C$ is removed,the current lags behind the voltage by a phase of $\pi / 3$. When the inductor $L$ is removed,the current leads the voltage by a phase of $\pi / 3$. What is the impedance of the circuit in $\Omega$?

$A$ circuit has a resistance of $11\,\Omega$,an inductive reactance of $25\,\Omega$,and a capacitive reactance of $18\,\Omega$. It is connected to an $AC$ source of $260\,V$ and $50\,Hz$. The current through the circuit (in amperes) is:

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

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 . . . . . . $min$.