Answered: -43.7 V Time Time 10 0 13 H 0.05 F

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter2: Fundamentals

Section: Chapter Questions

Problem 2.1MCQ: The rms value of v(t)=Vmaxcos(t+) is given by a. Vmax b. Vmax/2 c. 2Vmax d. 2Vmax

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Question

The attached image shows a circuit with an AC voltage source, a resistor, inductor, and capacitor connected in series. The circuit has the following characteristics:

Resistor resistance: 10 ohm

Capacitor capacitance: 0.05 F

Inductor inductance: 13 H

Current Amplitude: 4 A

Voltage amplitude across the source: 60 V

Frequency at the source: 0.3 Hz

Voltage amplitude across the resistor: 35 V

Voltage amplitude across the capacitor: 37 V

Voltage amplitude across the inductor: 80 V

(a) Calculate the RMS voltages from the amplitudes above. From the RMS voltages across the capacitor, inductor and resistor, calculate the RMS voltage of the AC source.

Hint: V_rms= V₀/sqrt(2)

V_rms= sqrt( (V_rms,R)² + (V_{rms, L} - V_{rms, C})² )

(b) Calculate the RMS value of the current

(c) Using the resistance, capacitance, inductance, and the frequency of the AC voltage, calculate the impedance Z. From this, and the previously measured value of V_rms, find the RMS value of the current in the circuit.

-43.7 V
Time
Time
10 0
13 H
0.05 F
Current (A)

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