For the RLC circuit shown in Fig. 16.88, find the complete response if v(0) = 100 V when the switch is closed.
Find the expression of voltage response
Answer to Problem 65P
The expression of voltage response
Explanation of Solution
Given data:
Refer to Figure 16.88 in the textbook.
The value of initial voltage across the capacitor
Formula used:
Write a general expression to calculate the impedance of a resistor in s-domain.
Here,
Write a general expression to calculate the impedance of an inductor in s-domain.
Here,
Write a general expression to calculate the impedance of a capacitor in s-domain.
Here,
Calculation:
The given circuit is redrawn as shown in Figure 1.
For time
Apply Laplace transform for
Substitute
Substitute
Substitute
Using element transformation methods with initial conditions convert the Figure 2 into s-domain.
Apply Kirchhoff’s voltage law for the circuit shown in Figure 3.
Substitute
Simplify the above equation to find
Refer to Figure 3, the voltage
Substitute
Assume,
Substitute equation (5) in equation (4).
Take partial fraction for equation (5).
The equation (7) can also be written as follows:
Simplify the above equation as follows:
Simplify the above equation as follows:
Equate the co-efficient of constant term in equation (8) to find
Simplify the above equation to find
Equate the co-efficient of
Simplify the above equation to find
Substitute
Equate the co-efficient of
Substitute
Equate the co-efficient of
Substitute
Simplify the above equation to find
Equate the co-efficient of
Substitute
Substitute the equation (11) in equation (10).
Simplify the above equation as follows:
Simplify the above equation to find
Substitute equation (11) in equation (12).
Simplify the above equation as follows:
Substitute the equation (13) in above equation to find
Simplify the above equation to find
Substitute
Substitute
Substitute
Substitute
Substitute
Simplify the above equation as follows:
Take inverse Laplace transform for above equation to find
Conclusion:
Thus, the expression of voltage response
Want to see more full solutions like this?
Chapter 16 Solutions
EBK FUNDAMENTALS OF ELECTRIC CIRCUITS
- A parallel RLC circuit has the following component values: R = variable, L = 25 mH, and C= 0.1 uF. If R is adjusted such that the circuit becomes critically damped, the value of R will be: O A. 2.5 K ohms O B. None of the other choices are correct O C. 50 ohms O D. 250 ohms O E. 500 ohmsarrow_forwardIn a seires RLC circuit with R=42, L=0.1 H, C=0.05 F, E= 110 V the circuit is said to be critically damped overdamped undamped underdampedarrow_forwardFor the above RLC circuit, select the state variables such that the stateequations of the system x = Ax+Bu y= Cx +Du can be written in form. Show it.arrow_forward
- Classwork Find the response i(t) of the RLC series circuit for t>0 R 1=0 V, C: Case 1 Case 2 Case 3 L=0.1H L=0.1H L=0.1H R=52 R=342 R=162 C=1/640F C=1/640F C=1/640F V=30V V=30V V=30Varrow_forwardIn a parallel RLC circuit with L= 8 H and C = 50 mF, find the value of R such that the system is critically damped. Оа. 6.125 0 Оb. 5.725 0 Oc. 6.325 0 Od. 5.925 2arrow_forwardA series RLC circuit is described by d²i di dt² L i +R + dt с = 2 Find the response when L = 0.5H, R = 492, and C = 0.2 F. Let i(0) = 1, di(0)/dt = 0.arrow_forward
- The nature of response in an RLC circuit is determined by the roots of the characteristic equation O True Falsearrow_forwardFind the solution of the following Differential Equations .by exact xdy – 4 ydx = 0arrow_forwardA series RLC circuit has the following component values: R = variable, L= 100 mH, and C= 0.1 uF. If R is adjusted such that the circuit becomes critically damped, the value of R will be: O A. 200 ohms O B. 20 K ohms OC.2K ohms O D. None of the other choices are correct O E. 400 ohmsarrow_forward
- 2. A branch voltage in an RLC circuit is described by dv dv + 4 + 8v = 48 dr dt If the initial conditions are v(0) = 0 = dv(0)/dt, find v(t). — Добавить файлarrow_forwardThe voltage accross 3-uF capacitor is shown .Deternine the current i(t) graphically and label all significat points v(t) 30 V 5 ms t(s)arrow_forwardIn a seires RLC circuit with R=0 0, L=1 H, C = 10-4 F, E= 100 sin(50t) V the circuit is said to be overdamped undamped underdamped critically dampedarrow_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,