Homework Answers
I have explained the use of Laplace Transform using an example of R,L,C circuit. This applies exactly in the same way to any circuit however complex it may be.
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Question 1 [10M a) Laplace transform is a very powerful tool for circuit analysis. i) Why...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following initial conditions in the inductor and capacitor: V.(0) - IV, 10) - 1A Follow the following steps in your solution. a) Draw the equivalent circuit in the Laplace Domain taking into account the initial conditions, and using the parallel model (see below) b) Use CDR or VDR to find Vo(s). c) Leave your answer in the Laplace Domain simplifying Vo(s) as a ratio of...
For the circuit shown in fig 2, Apply Laplace transform to find i) i1(t) and iz(t)...
For the circuit shown in fig 2, Apply Laplace transform to find i) i1(t) and iz(t) ii) Apply the initial and final value theorem iii) Explain your answer in part ii 10 12 100 V 30.02 H 350
TEE301/05 Question 3 (20 marks) An RLC circuit with a 1V DC source is shown in...
TEE301/05 Question 3 (20 marks) An RLC circuit with a 1V DC source is shown in Fig. 1: i(t) Vout - R-0.22 L-0.1 H C- 10 F Fig. 1 (a) List two properties of Laplace transform. Explain these two properties. [6 marks] (b) Assume that the initial inductor current is OA and initial capacitor voltage is 0.4 V 4 marks] (c) Determine the current, t) in time domain by performing inverse Laplace transform. [4 marks) determine the expression of the...
Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the...
Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the output is eo. 1). Find the state variable model. Take ec and IL as state variables (refer notes from Chapter-6). 2). Apply Laplace Transform on the state variable model (from part-1) and show that the transform of the output (eo) is given by the expression: 사스 ; if the initial conditions, L(0) and ec(0) are known. Note: ec(0)-eo(0) R L R L...
2. (11 pts) a) and b) Use the tables of Laplace transform pairs and properties to...
2. (11 pts) a) and b) Use the tables of Laplace transform pairs and properties to find the Laplace transforms for the following funetions: a) x(t)-(t-2) u(t) Electeie Caits 1 2s Ci) e2(1-2s) 2e2s Cii) Cin 1-2s 2 Civ) b) x(t)- d (3sin(3t)) u(t) dt -18s Ci) (s+9)2 9s CH) s+9 (ii) -3 (iv) +9 +9 e) and d) Find the inverse transform x(t) for each transform X(s) below. Assume all x(t) are multiplied by u(t) (left out for brevity)....
Please help solve, providing a detailed solution using the equations provided below and LaPlace transform (Use...
Please help solve, providing a detailed solution using the
equations provided below and
LaPlace transform (Use the table provided in the
link) to solve the differential equations obtained when working
through the question.
Link to the Laplace Transform Table:
https://ibb.co/TkrvbNH
Being given the following information, use the equations provided to find the steady-state current in the following RLC circuit. R=82 L= 0.5H C= 0.1F E(t) = 100 cos(2t) V knowing that at t = 0, i(0) = 0 Equations: UR...
I need help with this Dynamics II electrical system analysis. Please provide detailed explanation...
I need help with this Dynamics II electrical system
analysis.
Please provide detailed explanation and show work.
Thank you.
3. Find the transfer function E, (s)/E, (s) of the circuit below using impedance methods Find expressions for the natural frequency a, and the damping ratio ζ . ei(t) For L-0.2H, 2 mF RI 10 ohms, R2 20 ohms, use MATLAB to calculatew, and ζ and then also plot the unit step response of the system. Apply the final value theorem...
1) (40 pts total) Solving and order ODE using Laplace Transforms: Consider a series RLC circuit...
1) (40 pts total) Solving and order ODE using Laplace Transforms: Consider a series RLC circuit with resistor R, inductor L, and a capacitor C in series. The same current i(t) flows through R, L, and C. The voltage source v(t) is removed at t=0, but current continues to flow through the circuit for some time. We wish to find the natural response of this series RLC circuit, and find an equation for i(t). Using KVL and differentiating the equation...
I am currently learning about solving differential equations using Laplace transform and this question is from the chap...
I am currently learning about solving differential equations
using Laplace transform
and this question is from the chapter about Dirac-delta
function.
Thank you!
8. (a) Solve the initial-value problem dt and show that sint, n even L 0, n odd in the interval n <K(n +1)T. (b) Solve the initial-value problem dt and show that y()=(n+1) sint in the interval 2nπ〈t〈2(n+1)T. This example indicates why soldiers are instructed to break cadence when marching across a bridge. To wit, if the...
Consider the following statements. (i) Spring/mass systems and Series Circuit systems we covered are examples of...
Consider the following statements.
(i) Spring/mass systems and Series Circuit systems we covered
are examples of linear dynamical systems in which each mathematical
model is a second-order constant coefficient ODE along with initial
conditions at a specific time.
(ii) The following is an example of a piece-wise continuous
function
f (x) =
{
x
x ∈ Q
0
x ∈ R \ Q
(iii) It is unclear whether series solutions to ODEs even
exist, and knowing about series solutions to...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following initial conditions in the inductor and capacitor: V.(0) - IV, 10) - 1A Follow the following steps in your solution. a) Draw the equivalent circuit in the Laplace Domain taking into account the initial conditions, and using the parallel model (see below) b) Use CDR or VDR to find Vo(s). c) Leave your answer in the Laplace Domain simplifying Vo(s) as a ratio of...
For the circuit shown in fig 2, Apply Laplace transform to find i) i1(t) and iz(t) ii) Apply the initial and final value theorem iii) Explain your answer in part ii 10 12 100 V 30.02 H 350
TEE301/05 Question 3 (20 marks) An RLC circuit with a 1V DC source is shown in Fig. 1: i(t) Vout - R-0.22 L-0.1 H C- 10 F Fig. 1 (a) List two properties of Laplace transform. Explain these two properties. [6 marks] (b) Assume that the initial inductor current is OA and initial capacitor voltage is 0.4 V 4 marks] (c) Determine the current, t) in time domain by performing inverse Laplace transform. [4 marks) determine the expression of the...
Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the output is eo. 1). Find the state variable model. Take ec and IL as state variables (refer notes from Chapter-6). 2). Apply Laplace Transform on the state variable model (from part-1) and show that the transform of the output (eo) is given by the expression: 사스 ; if the initial conditions, L(0) and ec(0) are known. Note: ec(0)-eo(0) R L R L...
2. (11 pts) a) and b) Use the tables of Laplace transform pairs and properties to find the Laplace transforms for the following funetions: a) x(t)-(t-2) u(t) Electeie Caits 1 2s Ci) e2(1-2s) 2e2s Cii) Cin 1-2s 2 Civ) b) x(t)- d (3sin(3t)) u(t) dt -18s Ci) (s+9)2 9s CH) s+9 (ii) -3 (iv) +9 +9 e) and d) Find the inverse transform x(t) for each transform X(s) below. Assume all x(t) are multiplied by u(t) (left out for brevity)....
Please help solve, providing a detailed solution using the
equations provided below and
LaPlace transform (Use the table provided in the
link) to solve the differential equations obtained when working
through the question.
Link to the Laplace Transform Table:
https://ibb.co/TkrvbNH
Being given the following information, use the equations provided to find the steady-state current in the following RLC circuit. R=82 L= 0.5H C= 0.1F E(t) = 100 cos(2t) V knowing that at t = 0, i(0) = 0 Equations: UR...
I need help with this Dynamics II electrical system
analysis.
Please provide detailed explanation and show work.
Thank you.
3. Find the transfer function E, (s)/E, (s) of the circuit below using impedance methods Find expressions for the natural frequency a, and the damping ratio ζ . ei(t) For L-0.2H, 2 mF RI 10 ohms, R2 20 ohms, use MATLAB to calculatew, and ζ and then also plot the unit step response of the system. Apply the final value theorem...
1) (40 pts total) Solving and order ODE using Laplace Transforms: Consider a series RLC circuit with resistor R, inductor L, and a capacitor C in series. The same current i(t) flows through R, L, and C. The voltage source v(t) is removed at t=0, but current continues to flow through the circuit for some time. We wish to find the natural response of this series RLC circuit, and find an equation for i(t). Using KVL and differentiating the equation...
I am currently learning about solving differential equations
using Laplace transform
and this question is from the chapter about Dirac-delta
function.
Thank you!
8. (a) Solve the initial-value problem dt and show that sint, n even L 0, n odd in the interval n <K(n +1)T. (b) Solve the initial-value problem dt and show that y()=(n+1) sint in the interval 2nπ〈t〈2(n+1)T. This example indicates why soldiers are instructed to break cadence when marching across a bridge. To wit, if the...
Consider the following statements.
(i) Spring/mass systems and Series Circuit systems we covered
are examples of linear dynamical systems in which each mathematical
model is a second-order constant coefficient ODE along with initial
conditions at a specific time.
(ii) The following is an example of a piece-wise continuous
function
f (x) =
{
x
x ∈ Q
0
x ∈ R \ Q
(iii) It is unclear whether series solutions to ODEs even
exist, and knowing about series solutions to...
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