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1. Circuit analysis using phasor/impedance, complex power calculation: An RLC circuit is shown below. The reactance of the capacitor is 40 Ohm. The reactance of the inductor is 80 Ohm, and the resistor is 8 Ohm. The sending end voltage is v₁(t) = 345 cos(wt + 7) kV, where w = 2 · 60 rad/s. The receiving end voltage is v₂(t) = 345 cos(wt) kV. Ask: • What is the total impedance of the RLC circuit at 60 Hz? What are the sending end and receiving end voltage phasors in kV? • Please find the current through the line in phasor and in time-domain and in unit kA. • What is the complex power S₁? What is the complex power S₂? Please use a unit of MVA. • What is the power loss due to the resistor? What is the reactive power consumption by the inductor? How much reactive power is generated by the capacitor? . For the same sending end voltage and receiving end voltage, if the series capacitor is not installed, what is the real power delivered to the receiving end? Please compare this number with the one from the series compensated case, compare the current magnitude and the net reactance of the RL circuit and the RLC circuit, and state the advantage of series compensation. S, →>>> 777 RL с mm F S₂ টা

1. Circuit analysis using phasor/impedance, complex power calculation: An RLC circuit is shown below. The reactance of the capacitor is 40 Ohm. The reactance of the inductor is 80 Ohm, and the resistor is 8 Ohm. The sending end voltage is v₁(t) = 345 cos(wt + 7) kV, where w = 2 · 60 rad/s. The receiving end voltage is v₂(t) = 345 cos(wt) kV. Ask: • What is the total impedance of the RLC circuit at 60 Hz? What are the sending end and receiving end voltage phasors in kV? • Please find the current through the line in phasor and in time-domain and in unit kA. • What is the complex power S₁? What is the complex power S₂? Please use a unit of MVA. • What is the power loss due to the resistor? What is the reactive power consumption by the inductor? How much reactive power is generated by the capacitor? . For the same sending end voltage and receiving end voltage, if the series capacitor is not installed, what is the real power delivered to the receiving end? Please compare this number with the one from the series compensated case, compare the current magnitude and the net reactance of the RL circuit and the RLC circuit, and state the advantage of series compensation. S, →>>> 777 RL с mm F S₂ টা

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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1. Circuit analysis using phasor/impedance, complex power calculation: An RLC circuit is shown below. The reactance of the capacitor is 40 Ohm. The reactance of the inductor is 80 Ohm, and the resistor is 8 Ohm. The sending end voltage is v₁ (t) = 343 cos(wt + 7) kV, where w = 2 - 60 rad/s. The receiving end voltage is v₂ (t) = 3 cos (wt) kV. Ask: • What is the total impedance of the RLC circuit at 60 Hz? What are the sending end and receiving end voltage phasors in kV? • Please find the current through the line in phasor and in time-domain and in unit kA. • What is the complex power S₁? What is the complex power S₂? Please use a unit of MVA. • What is the power loss due to the resistor? What is the reactive power consumption by the inductor? How much reactive power is generated by the capacitor? • For the same sending end voltage and receiving end voltage, if the series capacitor is not installed, what is the real power delivered to the receiving end? Please compare this number with the one from the series compensated case, compare the current magnitude and the net reactance of the RL circuit and the RLC circuit, and state the advantage of series compensation. f Vs ~ S₁ RL C mm t S₂
Transcribed Image Text:1. Circuit analysis using phasor/impedance, complex power calculation: An RLC circuit is shown below. The reactance of the capacitor is 40 Ohm. The reactance of the inductor is 80 Ohm, and the resistor is 8 Ohm. The sending end voltage is v₁ (t) = 343 cos(wt + 7) kV, where w = 2 - 60 rad/s. The receiving end voltage is v₂ (t) = 3 cos (wt) kV. Ask: • What is the total impedance of the RLC circuit at 60 Hz? What are the sending end and receiving end voltage phasors in kV? • Please find the current through the line in phasor and in time-domain and in unit kA. • What is the complex power S₁? What is the complex power S₂? Please use a unit of MVA. • What is the power loss due to the resistor? What is the reactive power consumption by the inductor? How much reactive power is generated by the capacitor? • For the same sending end voltage and receiving end voltage, if the series capacitor is not installed, what is the real power delivered to the receiving end? Please compare this number with the one from the series compensated case, compare the current magnitude and the net reactance of the RL circuit and the RLC circuit, and state the advantage of series compensation. f Vs ~ S₁ RL C mm t S₂
Expert Solution
Step 1: Determine the given variables:-

Solution of all the five parts is as below:

The RLC circuit is shown below,

Electrical Engineering homework question answer, step 1, image 1

Capacitive space reactance comma space straight X subscript straight C equals 40 space straight capital omega. Inductive space reactance comma space straight X subscript straight L equals 80 space straight capital omega. Resistor comma space straight R equals 8 space space straight capital omega. Sending space end space voltage comma space straight v subscript 1 open parentheses straight t close parentheses equals fraction numerator 345 over denominator square root of 3 end fraction cos open parentheses straight omega straight t plus straight pi over 6 close parentheses space kV. Receiving space end space voltage comma space straight v subscript 2 open parentheses straight t close parentheses equals fraction numerator 345 over denominator square root of 3 end fraction cos open parentheses straight omega straight t close parentheses space kV. Where comma straight omega equals 2 straight pi times 60 space rad divided by sec.a

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