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A load of 40 -j 30 is connected to a source of 100 V with a phase angle of 30°, through a transmission line with an inductive reactance of 30 ohms. The total reactive power absorbed by the load is: O A. 187.5 vars O B. 177.5 vars O C. None of choices are correct O D. 184 vars OE. 120 vars

A load of 40 -j 30 is connected to a source of 100 V with a phase angle of 30°, through a transmission line with an inductive reactance of 30 ohms. The total reactive power absorbed by the load is: O A. 187.5 vars O B. 177.5 vars O C. None of choices are correct O D. 184 vars OE. 120 vars

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Question:** A load of 40 - j 30 is connected to a source of 100 V with a phase angle of \( 30^\circ \), through a transmission line with an inductive reactance of 30 ohms. The total reactive power absorbed by the load is: **Options:** - A. 187.5 vars - B. 177.5 vars - C. None of choices are correct - D. 184 vars - E. 120 vars (correct answer) **Explanation:** In this question, we are given a complex impedance load and asked to find the total reactive power absorbed by the load. The load is connected through a transmission line with a given inductive reactance. ### Solution Overview: Reactive power (measured in vars) can be calculated using the formula: \[ Q = V^2 \cdot \Im(\frac{1}{Z}) \] Where: - \(Q\) is the reactive power. - \(V\) is the voltage across the load. - \(Z\) is the complex impedance of the load. - \(\Im(\frac{1}{Z})\) represents the imaginary part of the complex admittance (inverse of impedance). ### Graphs/Diagrams: Since the problem text does not contain any graphical elements, and it is a text-based physics problem, no additional diagrams or graphs are needed to explain the solution. The problem can be solved through theoretical calculations. By examining the given options, the correct answer is indicated by the letter “E”, which corresponds to 120 vars.
Transcribed Image Text:**Question:** A load of 40 - j 30 is connected to a source of 100 V with a phase angle of \( 30^\circ \), through a transmission line with an inductive reactance of 30 ohms. The total reactive power absorbed by the load is: **Options:** - A. 187.5 vars - B. 177.5 vars - C. None of choices are correct - D. 184 vars - E. 120 vars (correct answer) **Explanation:** In this question, we are given a complex impedance load and asked to find the total reactive power absorbed by the load. The load is connected through a transmission line with a given inductive reactance. ### Solution Overview: Reactive power (measured in vars) can be calculated using the formula: \[ Q = V^2 \cdot \Im(\frac{1}{Z}) \] Where: - \(Q\) is the reactive power. - \(V\) is the voltage across the load. - \(Z\) is the complex impedance of the load. - \(\Im(\frac{1}{Z})\) represents the imaginary part of the complex admittance (inverse of impedance). ### Graphs/Diagrams: Since the problem text does not contain any graphical elements, and it is a text-based physics problem, no additional diagrams or graphs are needed to explain the solution. The problem can be solved through theoretical calculations. By examining the given options, the correct answer is indicated by the letter “E”, which corresponds to 120 vars.
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