Question 1

What happens at resonance in a series LCR circuit?

Accepted Answer

At resonance, the inductive and capacitive reactances are equal, so their reactive voltages cancel vectorially. The impedance becomes R, current is maximum for a fixed source voltage, and source voltage and current are in phase.

Question 2

Why is series LCR impedance not R + X_L + X_C?

Accepted Answer

Inductive and capacitive voltages have a 180-degree phase relationship, so they cancel partially or completely and must be added vectorially. The resulting magnitude is Z = sqrt(R² + (X_L - X_C)²).

Question 3

What is RMS voltage and why is it used for AC heating?

Accepted Answer

For a sinusoidal voltage, V_rms equals V0 divided by square root of 2, approximately 0.707 V0. Resistive heating depends on the effective RMS current and voltage, so average resistor power is calculated as P = I_rms²R.

Question 4

Why does the lamp stay dark in the ideal wattless-current circuit?

Accepted Answer

A pure inductor, pure capacitor or non-resonant lossless series L-C circuit may carry AC current without a resistor. The net voltage-current phase is 90 degrees in magnitude, so energy is exchanged between the electric and magnetic fields but average useful power over a cycle is zero.

Question 5

What happens when a capacitor is connected in a DC series circuit?

Accepted Answer

After the transient charging period, an ideal capacitor behaves as an open circuit for steady DC. Consequently, no steady DC current flows through a series circuit that contains that capacitor, even though current can flow briefly while the capacitor charges.

LCR Series Circuit: Resonance, Impedance & Power Factor

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