$A$ $44 \; mH$ inductor is connected to a $220 \; V, 50 \; Hz$ $AC$ supply,and a $60 \; \mu F$ capacitor is connected to a $110 \; V, 60 \; Hz$ $AC$ supply. What is the net power absorbed by each circuit over a complete cycle? Explain your answer.

(A) The net power absorbed in an $AC$ circuit is given by the formula $P = V_{rms} I_{rms} \cos \phi$,where $\phi$ is the phase difference between voltage and current.
$1$. For the inductive circuit:
In a pure inductor,the current lags behind the voltage by a phase angle of $\phi = 90^{\circ}$.
The power factor is $\cos 90^{\circ} = 0$.
Therefore,the net power absorbed $P = V_{rms} I_{rms} \times 0 = 0 \; W$.
$2$. For the capacitive circuit:
In a pure capacitor,the current leads the voltage by a phase angle of $\phi = 90^{\circ}$.
The power factor is $\cos 90^{\circ} = 0$.
Therefore,the net power absorbed $P = V_{rms} I_{rms} \times 0 = 0 \; W$.
In both cases,the net power absorbed over a complete cycle is zero because pure inductors and pure capacitors do not dissipate energy; they only store and release it.