Question

A resistance is connected to an AC source. If a capacitor is included in the series circuit, will the average power absorbed by the resistance increase or decrease? If an inductor of small inductance is also included in the series circuit, will the average power absorbed increase or decrease further?

Answer 1

When a capacitor is included in a series circuit, the impedance of the circuit,
$Z=\sqrt{R^2+{X_C}^2}$
The power absorbed by a resistor is given by,
$P={I_{rms}}^{2}R$
Since impedance increases due to introduction of a capacitor, the rms value of current I_rms will decrease and, hence, the power absorbed by the resistor will decrease.

When a small inductance is introduced in the circuit, the impedance of the circuit,
$Z=\sqrt{R^2+{\left(X_C-X_L\right)}^2}$
Since the impedance now decreases a little, the rms value of current will increase and, hence, the power absorbed by the resistor will increase.