In polar coordinates, what is the impedance...

Question 1 of 27070rpwJSlzbDlPbtQ0ugRvp

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?

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Question 1 of 27070

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?

🔍 Key Concepts

• Series RLC circuit impedance and how resistance and reactance combine • How to find net reactance when inductive and capacitive reactances are both present • Converting a rectangular impedance (R + jX) into polar form (magnitude and angle)

💭 Think About

• First, determine whether the total reactance is inductive or capacitive when a 300-ohm capacitor and 600-ohm inductor are in series. What is the net reactance value and its sign? • Once you have R and X, how do you calculate the magnitude of the impedance using the Pythagorean theorem? • How is the phase angle of the impedance related to the arctangent of X over R, and what does the sign of X tell you about the angle direction?

✅ Before You Answer

• Compute the net reactance: XL - XC (or XC - XL) carefully, including the sign • Use $|Z| = \sqrt{R^2 + X^2}$ with R = 400 ohms and your net X value; check that your magnitude matches one of the choices • Compute the phase angle using $\theta = \tan^{-1}(X/R)$ and make sure the sign of X (inductive vs capacitive) matches the angle direction in polar form