971 Solving State Variable Equations With zero input, a series RLC circuit can be described by the following coupled first order equations in the inductor current iLt and capacitor voltage vCt (a) Transform these equations into the s domain and solve for the transforms ILs and VCs in terms of the initial conditions iL0 I0 and vC0 V0 (b) Find iLt and vCt for R 100 , L 100mH, C 1 F, I0 10 mA, and V0 15V dt dvc(1)i (1) C di(t) R dt vc(1) iL (1)

The Answer is in the image, click to view ...

Question: 971 Solving State Variable Equations With zero input, a series RLC circuit can be described by the following coupled first-order equations in the inductor current

9–71 Solving State Variable Equations With zero input, a series RLC circuit can be described by the following coupled first-order equations in the inductor current iLðtÞ and capacitor voltage vCðtÞ.

dt dvc(1)i (1) C di(t) R dt = -vc(1) - iL (1)

(a) Transform these equations into the s domain and solve for the transforms ILðsÞ and VCðsÞ in terms of the initial conditions iLð0Þ = I0 and vCð0Þ =V0.

(b) Find iLðtÞ and vCðtÞ for R= 100 Ω, L= 100mH, C = 1 μF, I0 = 10 mA, and V0 =15V.

dt dvc(1)i (1) C di(t) R dt = -vc(1) - iL (1)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Systems Analysis And Design Questions!

Solving State Variable Equations With zero input, a series RLC circuit can be described by the following coupled first-order equations in the inductor current iL(t) and capacitor voltage vC(t). dvCt...

796 Solving Differential Equations with MATLAB MATLAB has a built-in function for solving ordinary differential equations called dsolve. We can use this function to quickly explore the solution to a...

Solving Differential Equations with MATLAB MATLAB has a built-in function for solving ordinary differential equations called dsolve. We can use this function to quickly explore the solution to a...

Consider the following system described below ( parameters and inputs are in SI units ) : I m = 0 . 4 , R : = 0 . 1 8 I p = 0 . 2 , k = 3 0 m r : = 6 , b : = 2 0 T ( t ) = 2 , Note: b is the damping...

[ 1 0 points ] Consider the following fluid system. The state variable equations are: A 1 h 1 = q m i - g h 1 - g h 2 R 1 A 2 h 2 = g h 1 - g h 2 R 1 - g h 2 R 2 Assume that g = 1 0 m 2 s , = 1 , R 1...

Inverted Pendulum Fig. 1 shows a cart on wheels that can be moved back and forth to balance the stick that is supported by a frictionless pivot at the base of the stick. The system also includes an...

Consider the ball and beam system [10] shown in Figure 5.132, in which $I$ and $I_{\mathrm{b}}$ are the mass moments of inertia of the beam and the ball, respectively, $m$ is the mass of the...

Assume a system can be represented by the following state variable equations. The variable d 0 is input to the system. Write the equations = Ax + Bu in format. Put equations into MATLAB, show command...

Consider the ball and beam system shown in the figure. In the system, I and I b are the mass moments of inertia of the beam and the ball, respectively, m is the mass of the ball, and r is the radius...

In the system, the total mass of the vehicle is 4000kg, the moment of inertia of the vehicle around c.g. is J = mr- (r = 0.64m-), 1= 1.4m, and 12 = 0.9m, friction coefficient c for each tire-...

Describe the current convergence efforts of the FASB and IASB in the area of accounting for taxes.

Edison Mfg. needs to borrow $50,000 for six months. If the annual interest rate is 15%, what is the APY of a loan with interest paid in arrears and a 10% compensating balance? Edison Mfg. needs to...

Evaluate limx 4 ( cot ( 8 3 x 3 csc ( 4 x 3 ) + 4 ) ) . Enter an exact answer.

Explain the difference between indemnity value and replacement value.

Do a source transformation at terminals A and B for each practical source in Figure P246.AppendixLO1 (A) B 100 A (a) www 5 + B (b) FIGURE P2-46 5 mA 5 V

Find the equivalent practical voltage source at terminals A and B in Figure P247.AppendixLO1 502 (A) o w 10 15 A Bo FIGURE P2-47

In Figure P248 the i-v characteristic of network N is v 50i 5 V. Find the equivalent practical current source for the network.AppendixLO1 i + (A) N V FIGURE P2-48 (B)

On January 1, 2021, Kendall Inc. began construction of an automated cattle feeder system. The system was finished and ready for use on September 30, 2022. Expenditures on the project were as follows...

7) If I spent $20,000 on an allotment and it was giving me 21,000,000 gross impressions (GI) on a weekly basis, what is my cost per 1,000 (GI)? a. $95 b. $9.50 c. $.95 d. $.00095

d Required Information Use the following information for the Exercises below. (Algo) (The following information applies to the questions displayed below] On December 1, Jasmin Ernst organized Ernst...