The current
Answer to Problem 4.10HP
The expression for the current through the inductor for different time interval is
Explanation of Solution
Calculation:
The given diagram is shown in Figure 1
The conversion from
The conversion from
The conversion from
The conversion from
The conversion from
The conversion from
The conversion from
The conversion from
From the graph the expression for the voltage between the points
From the graph the expression for the voltage between the points
From the graph the expression for the voltage at
The expression for the voltage across the inductor is given by,
The expression for the current through the inductor is given by,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The expression for the current through the inductor is given by,
Conclusion:
Therefore, the expression for the current through the inductor for different time interval is
Want to see more full solutions like this?
Chapter 4 Solutions
Principles and Applications of Electrical Engineering
- The current waveform shown in Figure P4.23 flowsthrough a 2-H inductor. Plot the inductor voltage vL(t).arrow_forwardWe know that the capacitor shown in Figure P4.11 is charged to a voltage of 10 V priorto t=0.a. Find expressions for the voltage across the capacitor vC(t) and the voltage across theresistor vR(t) for all time.b. Find an expression for the power delivered to the resistor.c. Integrate the power from t=0 to t=∞ to find the energy delivered.d. Show that the energy delivered to the resistor is equal to the energy stored in thecapacitor prior to t=0.arrow_forwardConsider the circuit shown in Figure P4.40. A voltmeter (VM) is connected across the inductance. The switch has been closed for a long time. When the switch is opened, an arc appears across the switch contacts. Explain why. Assuming an ideal switch and inductor, what voltage appears across the inductor when the switch is opened? What could happen to the voltmeter when the switch opens?arrow_forward
- The plot of time-dependent voltage is shown inFigure P4.12. The waveform is piecewise continuous.If this is the voltage across a capacitor and C = 80 μF,determine the current through the capacitor. How cancurrent flow “through” a capacitor?arrow_forwardIf the plots shown in Figure P4.19 are the voltageacross and the current through an ideal inductor,determine the inductance.arrow_forwardFor the circuit shown in Figure (4.a): i) Find the voltage across the capacitor in polar form. ii) Draw the phasor diagram relationship of Vc and Vs. iii) Is this circuit pre-dominantly inductive or capacitive? Why?arrow_forward
- Determine and plot as a function of time thecurrent through a component if the voltage across ithas the waveform shown in Figure P4.17 and thecomponent is aa. Resistor R = 7 b. Capacitor C = 0.5 μFc. Inductor L = 7 mHarrow_forwardP4.11. We know that the capacitor shown in Figure P4.11 O is charged to a voltage of 10 V prior to t a. Find expressions for the voltage across the capacitor vc(t) and the voltage across the resistor vR(t) for all time. b. Find an expression for the power delivered to the resistor. c. Integrate the power from t = 0 to t = ∞ to find the energy delivered. 0. d. Show that the energy delivered to the resistor is equal to the energy stored in the capacitor prior to t = 0. t = 0 R = 100 N 100 μF UR(1)arrow_forwardThe initial voltage across the capacitor shown in Figure P4.3 is v C ( 0+ )=0. Find an expression for the voltage across the capacitor as a function of time, and sketch to scale versus timearrow_forward
- 3 Determine the voltage across the inductor in the circuit shown in Figure P4.63. 3 mH Vz(f) Vs(f) = 24 cos(1,000?) E wwarrow_forwardThe capacitor model we have used so far has beentreated as an ideal circuit element. A more accuratemodel for a capacitor is shown in Figure P4.67. Theideal capacitor, C, has a large “leakage” resistance, RC,in parallel with it. RC models the leakage currentthrough the capacitor. R1 and R2 represent the leadwire resistances, and L1 and L2 represent the lead wireinductances.a. If C = 1 μF, RC = 100 MΩ, R1 = R2 = 1 μΩ andL1 = L2 = 0.1 μH, find the equivalent impedanceseen at the terminals a and b as a function offrequency ω.b. Find the range of frequencies for which Zab iscapacitive, i.e., Xab > 10|Rab.Hint: Assume that RC is is much greater than 1/wC so thatyou can replace RC by an infinite resistance in part b.arrow_forwardIn Figure P4.64, let R=500 Ω. Using the inductor current, derive the Characteristic Equation.arrow_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,