FCC Exam Question: 3-17B4

In polar coordinates, what is the impedance of a network composed of a 300-ohm-reactance capacitor, a 600-ohm-reactance inductor, and a 400-ohm resistor, all connected in series?

A. 500 ohms, /37 degrees
B. 400 ohms, /27 degrees
C. 300 ohms, /17 degrees
D. 200 ohms, /10 degrees
Correct Answer: A

Explanation: In a series RLC circuit, the total reactance (X) is the difference between the inductive reactance (XL) and the capacitive reactance (XC). Here, X = XL - XC = 600Ω - 300Ω = 300Ω. Since XL is greater than XC, the circuit is inductively reactive. The total impedance (Z) is the vector sum of the resistance (R) and the total reactance (X), calculated using the Pythagorean theorem: Z = √(R² + X²) = √(400² + 300²) = √(160000 + 90000) = √250000 = 500Ω. The phase angle (θ) represents the phase difference between the voltage and current. It's calculated using the arctangent of the ratio of total reactance to resistance: θ = arctan(X/R) = arctan(300/400) = arctan(0.75) ≈ 36.87°, which rounds to 37 degrees. Since the total reactance is positive (inductive), the angle is positive. Thus, the impedance in polar coordinates is 500 ohms with a phase angle of 37 degrees, commonly written as 500 ohms, /37 degrees.

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Includes Elements 1, 3, 6, 7R, 8, and 9.