FCC Exam Question: 3-16B4

In rectangular coordinates, what is the impedance of a network composed of a 1.0-millihenry inductor in series with a 200-ohm resistor, at 30 kHz?

A. 200 - j188
B. 200 + j188
C. 188 + j200
D. 188 - j200
Correct Answer: B

Explanation: The impedance of a series circuit in rectangular coordinates is expressed as Z = R + jX, where R is the resistance and X is the reactance. For an inductor, the reactance (XL) is positive, contributing a +jXL term. First, calculate the inductive reactance (XL) using the formula XL = 2πfL: * R = 200 Ω * L = 1.0 mH = 0.001 H * f = 30 kHz = 30,000 Hz XL = 2 * π * (30,000 Hz) * (0.001 H) XL ≈ 188.5 Ω Since the resistor and inductor are in series, the total impedance is Z = R + jXL. Therefore, Z = 200 + j188.5 Ω. Option B, 200 + j188, is the closest match to this calculation. Options A and D are incorrect because an inductor adds a positive imaginary (inductive) reactance, not a negative one. Options C and D incorrectly swap the real (resistance) and imaginary (reactance) components.

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