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?

Power after addition of capacitor will decrease. Power after addition of inductor will increase.

The impedance of the circuit after introduction of capacitor is given by … (i), where R = resistance, XC = capacitive reactance.


Now, average power is given by … (ii), where irms = rms value of current, R = resistance


Since irms decreases with increase in impedance, hence on the introduction of a capacitor, the average power absorbed by the resistance will also decrease. (Ans)


Now, the impedance of an LCR circuit is given by … (iii), where R = resistance, XL = inductive reactance, XC = capacitive reactance.


Hence, compared to Z1, the value of Z2 is less and the rms value of current is greater in this case. Therefore, if a small inductance is also introduced in the circuit, the average power absorbed increases. (Ans)


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