In polar coordinates, what is the impedance...

Question 1 / 27070C7vgFSBS4mrbtNn9hsuO

Question 1 of 27070C7vgFSBS4mrbtNn9hsuO

In polar coordinates, what is the impedance of a network composed of a 100-ohm-reactance inductor in series with a 100-ohm resistor?

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Question 1 of 27070

In polar coordinates, what is the impedance of a network composed of a 100-ohm-reactance inductor in series with a 100-ohm resistor?

🔍 Key Concepts

• Series R-L impedance represented as a right triangle on the complex plane • Conversion from rectangular form (R + jX) to polar form (magnitude and angle) • Relationship between resistance, reactance, and impedance in AC circuits

💭 Think About

• How do you combine the 100-ohm resistor and the 100-ohm inductive reactance when they are in series: do you add directly, or treat them as perpendicular components? • What is the formula for the magnitude of impedance when you have a real part (R) and an imaginary part (X)? • Given R and X are equal, what special angle does that create in a right triangle, and which answer choice has that angle?

✅ Before You Answer

• Confirm that you are treating the resistor as the real part and the inductor’s reactance as the imaginary part of the impedance • Use the Pythagorean theorem to compute the magnitude of the impedance from R and X • Use the arctangent function to find the phase angle and then match both magnitude and angle to one of the answer choices

Question 1 of 27070

In polar coordinates, what is the impedance of a network composed of a 100-ohm-reactance inductor in series with a 100-ohm resistor?

121 ohms, /35 degrees

141 ohms, / 45 degrees

161 ohms, /55 degrees

181 ohms, /65 degrees