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Problem 5: A 500 resistor and 100 mH inductor are wired in series. What is their combined impedance at 150 rad/s? Express the combined impedance in both rectangular and polar formats. |Zeg (150 rad/s) = 50+j152-52.20-16.70° 2 eq

Problem 5: A 500 resistor and 100 mH inductor are wired in series. What is their combined impedance at 150 rad/s? Express the combined impedance in both rectangular and polar formats. |Zeg (150 rad/s) = 50+j152-52.20-16.70° 2 eq

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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**Problem 5:** A 50Ω resistor and 100 mH inductor are wired in series. What is their combined impedance at 150 rad/s? Express the combined impedance in both rectangular and polar formats. The solution to this problem is shown as: \[ Z_{\text{eq}}(150 \, \text{rad/s}) = 50 + j15 \, \Omega = 52.20 \angle 16.70^\circ \, \Omega \] ### Explanation: 1. **Rectangular Format**: - The impedance \( Z_{\text{eq}} \) is expressed as the sum of a real part (resistance) and an imaginary part (reactance): \( 50 + j15 \, \Omega \). - Here, \( 50 \, \Omega \) is the resistive component, and \( j15 \, \Omega \) is the inductive reactance. 2. **Polar Format**: - The impedance is also represented in polar format as \( 52.20 \angle 16.70^\circ \, \Omega \). - This format shows the magnitude of the impedance as 52.20 Ω and the phase angle as 16.70 degrees.
Transcribed Image Text:**Problem 5:** A 50Ω resistor and 100 mH inductor are wired in series. What is their combined impedance at 150 rad/s? Express the combined impedance in both rectangular and polar formats. The solution to this problem is shown as: \[ Z_{\text{eq}}(150 \, \text{rad/s}) = 50 + j15 \, \Omega = 52.20 \angle 16.70^\circ \, \Omega \] ### Explanation: 1. **Rectangular Format**: - The impedance \( Z_{\text{eq}} \) is expressed as the sum of a real part (resistance) and an imaginary part (reactance): \( 50 + j15 \, \Omega \). - Here, \( 50 \, \Omega \) is the resistive component, and \( j15 \, \Omega \) is the inductive reactance. 2. **Polar Format**: - The impedance is also represented in polar format as \( 52.20 \angle 16.70^\circ \, \Omega \). - This format shows the magnitude of the impedance as 52.20 Ω and the phase angle as 16.70 degrees.
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