Question 1 of 270707rZZTqYSSqiwhXdS2USz

In polar coordinates, what is the impedance of a network comprised of a 400-ohm-reactance inductor in parallel with a 300-ohm resistor?

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Question 1 of 27070
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In polar coordinates, what is the impedance of a network comprised of a 400-ohm-reactance inductor in parallel with a 300-ohm resistor?

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🔍 Key Concepts

• Impedance of a resistor vs. impedance of an inductor in rectangular form • Parallel combination of impedances using admittance (1/Z) • Conversion from rectangular impedance to polar form (magnitude and angle)

💭 Think About

• First, write the impedance of the resistor and the inductor separately in complex (rectangular) form. What are they on the R–jX plane? • For parallel circuits, it is often easier to work with admittance (Y = 1/Z). How do you add admittances of parallel elements, and then convert back to total impedance? • Once you have the total impedance in rectangular form, how do you find its magnitude and phase angle to express it in polar form?

✅ Before You Answer

• Be sure the inductor’s reactance is represented with the correct sign (inductive reactance is +jX). • When combining parallel elements, confirm you are adding admittances (1/Z) rather than impedances directly. • After converting back to impedance, double-check both the magnitude (using Pythagorean theorem) and the angle (using arctangent with correct quadrant).