Question
What is the magnitude of the impedance of a series RLC circuit at resonance?
Answer Options
- A) High, compared to the circuit resistance
- B) Approximately equal to capacitive reactance
- C) Approximately equal to inductive reactance
- D) Approximately equal to circuit resistance
Correct Answer: D
Explanation
In a series RLC circuit, the total impedance (Z) is the vector sum of the resistance (R) and the net reactance (X_{net}), given by the formula Z = \sqrt{R^2 + X_{net}^2}. The net reactance X_{net} is the difference between the inductive reactance (X_L) and the capacitive reactance (X_C), X_{net} = X_L - X_C.
At the resonant frequency, the magnitudes of the inductive and capacitive reactances are equal (X_L = X_C), meaning the net reactance X_{net} becomes zero. Therefore, the total impedance equation simplifies to Z = \sqrt{R^2 + 0^2} = R. This means that the magnitude of the impedance of a series RLC circuit at resonance is at its minimum value, and it is approximately equal to the circuit resistance.
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