Question

In an RLC circuit, explain why Xl increases with frequency while Xc decreases with frequency.

Answer 1

Of course we are talking of AC current.
For an inductor when the current changes there is an induced counter current that opposes the applied current. This counter current effectively reduces the net current in the inductor which if like increasing its impedance. This counter current increases with the rate of change of the applied current. So as the frequency increases the rate of change of the current also increase reducing the net current flowing in the coil.

For a capacitor the charging current decreases with time. Thus while the capacitor is charging if the rate of change of the current is slow the capacitor is "filling up with charge" which exponentially slows down as time goes on. If the current is reversed before the capacitor is charged the average current will be higher than if it is left charging. Thus since as the frequency increases the current reverses before the capacitor is fully charged the net average current charging the capacitor is higher effectively making it look like a better conductor, that is like making the capacitor have a lower impedance.