A capacitor of unknown capacitance, a resistor of 100 V and an inductor of self-inductance L5(4/p²) henry are connected in series to an ac source of 200V and 50 Hz. Calculate the value of the capacitance and impedance of the circuit when the current is in phase with the voltage. Calculate the power dissipated in the circuit.

Question

A capacitor of unknown capacitance, a resistor of 100 V and an inductor of self-inductance L5(4/p²) henry are connected in series to an ac source of 200V and 50 Hz. Calculate the value of the capacitance and impedance of the circuit when the current is in phase with the voltage. Calculate the power dissipated in the circuit.

Philoid · Accepted Answer

It is given that the current is in phase with the voltage. Hence, we have a resonance condition where the capacitive reactance (X_C) is equal to the inductive reactance(X_L). So, the frequency is given by

Given, and

As we have resonance, the impedance Z is equal to the resistance(R).

The voltage of the ac source is V=200V. Therefore, power dissipated(P) is

.