Z = Impedance R = Resistance XL = Inductive Reactance Xc = Capacitive Reactance What is the impedance of an ac-series circuit consisting of an inductor with a reactance of 10 ohms, a capacitor with a reactance of 4 ohms, and a resistor with a resistance of 8 ohms?

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Enhance your understanding of the fundamentals of electricity with the AMT General Exam. Study with multiple-choice questions crafted to improve your knowledge and confidence. Prepare effectively for your success!

Multiple Choice

Z = Impedance R = Resistance XL = Inductive Reactance Xc = Capacitive Reactance What is the impedance of an ac-series circuit consisting of an inductor with a reactance of 10 ohms, a capacitor with a reactance of 4 ohms, and a resistor with a resistance of 8 ohms?

Explanation:
In an AC series circuit, impedance combines resistance and net reactance as the magnitude of a vector: Z = sqrt(R^2 + (XL - Xc)^2). Here, the net reactance is 10 ohms minus 4 ohms, which is 6 ohms, and the resistance is 8 ohms. So Z = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 ohms. The 10-ohm result reflects the fact that the impedance is the vector combination of resistance and net reactance in a series RLC circuit.

In an AC series circuit, impedance combines resistance and net reactance as the magnitude of a vector: Z = sqrt(R^2 + (XL - Xc)^2). Here, the net reactance is 10 ohms minus 4 ohms, which is 6 ohms, and the resistance is 8 ohms. So Z = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 ohms. The 10-ohm result reflects the fact that the impedance is the vector combination of resistance and net reactance in a series RLC circuit.

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