What is the magnitude of the impedance of a series network consisting of a 400-ohm resistor, a 600-ohm inductor reactance, and a 300-ohm capacitor reactance?

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Multiple Choice

What is the magnitude of the impedance of a series network consisting of a 400-ohm resistor, a 600-ohm inductor reactance, and a 300-ohm capacitor reactance?

In a series circuit with a resistor and reactive elements, the impedance combines like perpendicular components: the resistance forms one leg and the net reactance forms the other. The magnitude of the impedance is found from the Pythagorean relation |Z| = sqrt(R^2 + (X_L − X_C)^2). Here, the resistor is 400 Ω, the inductive reactance is 600 Ω, and the capacitive reactance is 300 Ω. The net reactance is X_L − X_C = 600 − 300 = 300 Ω. Therefore, |Z| = sqrt(400^2 + 300^2) = sqrt(160000 + 90000) = sqrt(250000) = 500 Ω. This shows why the result is 500 ohms: you must combine the resistive and net reactive parts as perpendicular components, not simply add their magnitudes.

In a series circuit with a resistor and reactive elements, the impedance combines like perpendicular components: the resistance forms one leg and the net reactance forms the other. The magnitude of the impedance is found from the Pythagorean relation |Z| = sqrt(R^2 + (X_L − X_C)^2).

Here, the resistor is 400 Ω, the inductive reactance is 600 Ω, and the capacitive reactance is 300 Ω. The net reactance is X_L − X_C = 600 − 300 = 300 Ω. Therefore, |Z| = sqrt(400^2 + 300^2) = sqrt(160000 + 90000) = sqrt(250000) = 500 Ω.

This shows why the result is 500 ohms: you must combine the resistive and net reactive parts as perpendicular components, not simply add their magnitudes.

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