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

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Multiple Choice

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

In a series circuit, impedances add with their real and imaginary parts combined: the resistor contributes a real part, the inductor contributes a positive imaginary part, and the capacitor contributes a negative imaginary part. So the total impedance is Z = 400 + j(600) + (-j300) = 400 + j300 ohms. The magnitude is sqrt(400^2 + 300^2) = 500 ohms. The phase is arctan(Imag/Real) = arctan(300/400) ≈ 36.9 degrees. Therefore, the impedance in polar form is about 500 ohms at +37 degrees, which matches a net inductive result since XL > XC.

In a series circuit, impedances add with their real and imaginary parts combined: the resistor contributes a real part, the inductor contributes a positive imaginary part, and the capacitor contributes a negative imaginary part. So the total impedance is Z = 400 + j(600) + (-j300) = 400 + j300 ohms. The magnitude is sqrt(400^2 + 300^2) = 500 ohms. The phase is arctan(Imag/Real) = arctan(300/400) ≈ 36.9 degrees. Therefore, the impedance in polar form is about 500 ohms at +37 degrees, which matches a net inductive result since XL > XC.

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