An alternating supply of $220\,V$ is applied across a circuit with resistance $22\,\Omega$ and impedance $44\,\Omega$. The power dissipated in the circuit is.........$W$.

$A$ $LCR$ series circuit driven with $V_{rms} = 90 \text{ V}$ at frequency $f_d = 30 \text{ Hz}$ has resistance $R = 80 \text{ }\Omega$, an inductance with inductive reactance $X_L = 20.0 \text{ }\Omega$ and capacitance with capacitive reactance $X_C = 80.0 \text{ }\Omega$. The power factor of the circuit is . . . . . . .

The power factor of a good choke coil is

In an $AC$ circuit,$V$ and $I$ are given by $V = 150 \sin(150t) \, V$ and $I = 150 \sin(150t + \frac{\pi}{3}) \, A$. The power dissipated in the circuit is $W$.

$(a)$ For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.
$(b)$ Power factor can often be improved by the use of a capacitor of appropriate capacitance in the circuit. Explain.

The instantaneous values of alternating current and voltage in a circuit are given as $I = \frac{1}{\sqrt{2}} \sin(100\pi t)$ and $E = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3})$. The average power in watts consumed in the circuit is: