Question 17: AC fundamentals

Question

A series LCR circuit having $\mathrm{R}=44 \Omega, \mathrm{~L}=2 \mathrm{H}$ and $\mathrm{C}=25 \mu \mathrm{~F}$ is connected to a variable frequency of 220 V . What is the average power transferred to the circuit in one complete cycle if the frequency of supply equals the natural frequency of the circuit?

Accepted Answer

At resonance $X_L = X_C$, so the net impedance is purely resistive:
$ Z = R = 44\ \Omega. $
The rms current is
$ I_{m rms} = \frac{V_{m rms}}{R}              = \frac{220}{44}              = 5\ 	ext{A}. $
The average power (over one cycle) is
$ P = V_{m rms}\,I_{m rms}\cos\phi   = V_{m rms}\,I_{m rms}   = \frac{V_{m rms}^2}{R}   = \frac{220^2}{44}   = 1100\ 	ext{W}   = 1.1\ 	ext{kW}. $
Answer: Option C (1.1 kW).

Answer

2.1 kW

Answer

4.2 kW

Answer

1.1 kW

Answer

1.2 kW

AC fundamentals

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