
Concept explainers
Find the current through the inductor

Answer to Problem 39P
The current through the inductor
Explanation of Solution
Given data:
Refer to Figure 17.75(a) and 17.75(b) in the textbook.
The inductor L is
The capacitor
Formula used:
Write the general expression for Fourier series expansion.
Write the expression to calculate the fundamental angular frequency.
Here,
Calculation:
Refer to Figure 17.73(a) in the textbook.
The source voltage
The time period of Figure 17.75(a) is,
Substitute 2 for T in equation (2) to find the angular frequency
Finding the Fourier coefficient
Applying equation (3) in equation (4) as follows,
The above equation becomes,
Finding the Fourier coefficient
Applying equation (3) in equation (5) as follows,
Finding the Fourier coefficient
Applying equation (3) in equation (6) as follows,
Simplify the equation as follows,
The above equation becomes,
Substituting the Fourier coefficients in equation (1) as follows,
Refer to Figure 17.75(b) in the textbook.
For the DC component, the current
The inductor acts as a short circuit for DC.
For the kth harmonic,
Consider Figure 17.75(b) for AC analysis.
The impedance of the inductor is calculated as follows,
Substitute
The impedance of the capacitor is calculated as follows,
Substitute
The modified circuit is shown in Figure 1.
In Figure 1, the impedance is,
Simplify the above equation as follows,
The impedance
Substitute
The current
Substitute
The current
Substitute
Simplify the equation as follows,
The magnitude and phase angle of the current
In the time domain,
Where,
The phase angle
And,
The current
Conclusion:
Thus, the current through the inductor
Want to see more full solutions like this?
Chapter 17 Solutions
Fundamentals of Electric Circuits
- Answer all the questions What is the minimum value of capacitor C1 required such that Vfiltered does not drop below 8 V? Use the design equation(but make sure you use the right “frequency” and the correct ripple voltage). Show your calculations. Display your circuit in circuit js. Display Vsecondary (can use the voltage across the added 100 kΩ resistor) and Vfiltered in a “Combined Scope”. Display VDC in a separate scope: a) Turn on “Max Scale”, “Show Peak Value” and “Show Negative Peak Value”: b) Run the simulator and adjust the window and simulation speed and time step to be able to see a couple of cycles. Include a screen capture Document the minimum and maximum values for Vfiltered in your lab report. Is Vfiltered maintained to be above 8 V? By how much? Why? Explain the waveform shape captured Vfiltered. It may help your understanding to rerun the simulation with C1 removed and compare that waveform for Vfiltered to that capturedarrow_forwardA Three-phase, 3.3 kV, Y connected, 500 kVA, 16 salient pole rotor alternator. The direct and quadrature axis synchronous reactance are 8 and 50/ph respectively. The machine is supplying a load of 350 kVA at 0.8 power factor lagging, Determine: 1. Power angle. 2. Percentage Voltage regulation. 3. Developed power. 4. Reluctance powerarrow_forwardA Three-phase, 12 pole, Y-connected alternator has 108 slots and 14 conductors per slot. The windings are (5/6th) pitched. The flux per pole is 57 mWb distributed sinusoidally over the pole. If the machine runs at 500 r.p.m., determine the following: (a) The frequency of the generated e.m.f., (b) The distribution factor, (c) The pitch factor, and (d) The phase and line values of the generated e.m.f.?arrow_forward
- Many machines, such as lathes, milling machines, and grinders, are equipped with tracers to reproduce the contours of templates. The figure is a schematic diagram of a hydraulic tracer in which the tool duplicates the shape of the template on the workpiece. a) Explain how the system works. b) Draw a block diagram and identify the system's elements. c) Classify the control system. Oil under pressure Template Style Tool Piece of workarrow_forward2. Refrigerators to maintain the product at a given temperature have a control system. a) Explain how the control system is or how you think it should be (Make a diagram). b) Make the typical block diagram of a control system and identify the components in the refrigerator system. c) Classify the control system.arrow_forward3. Internal combustion engines require a cooling system to function properly, which maintains the engine temperature at an appropriate value. Neither too high nor too low. There are several systems to control this temperature, the two best known are: • The classic one that uses a thermostat that regulates the flow of coolant (water), and where the fan is mechanically coupled to the engine. • In more recent vehicles, in addition to the thermostat, a temperature controller is used that turns an electric fan on and off. Select one of the two systems mentioned above and: a) Explain how it works, using diagrams. b) Make the typical block diagram of a feedback control system, identifying the components of the system. c) Classify the control system.arrow_forward
- A 3-phase, star connected, 10 kVA, 380 V, salient pole alternator with direct and quadrature axis reactances of 15 and 8 0/ph respectively, delivers full-load current at 0.8 power factor lagging. Neglect the armature resistance. Determine the following: (a) The load angle, (b) The direct axis and quadrature axis components of armature current, (c) E.M.F induced voltage of the alternator, (d) The voltage regulation, and (e) The developed power by the alternator?arrow_forwardA 2000 kVA,Y- connected alternator gives an open circuit line voltage of 3.3 kV for a field current of 65 A. For same field current the short circuit current is being equal to full load current. Calculate the full load voltage regulation at both 0.8 lagging p.f. and unity p.f., neglect armature resistance?arrow_forwardDon't use ai to answer I will report you answerarrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,





