Explanation Calculation: The given diagram is shown in Figure 1. The switch is open for long duration at t < 0 , thus the inductor is open circuited. Redraw the circuit diagram at t = 0 − . The initial current through the inductor is given by, i L ( 0 − ) = i L ( 0 + ) Substitute 0 A for i L ( 0 + ) in the above equation. i L ( 0 − ) = 0 A Modify the circuit diagram for t > 0 . The required diagram is shown in Figure 2. Apply KVL in the above circuit. 2 i L ( t ) + 1 d i L ( t ) d t = 5 e − 2 t cos ( 3 t ) ....... (1) The complete solution for the differential equation is given by, i L ( t ) = i C ( t ) + i p ( t ) .......(2) From equation (1) the complementary solution to the equation is calculated by equating the forced term to 5 e − 2 t cos ( 3 t ) equal to zero. Substitute 0 for 5 e − 2 t cos ( 3 t ) and i C ( t ) for i L ( t ) in equation (1). 2 i C ( t ) + 1 d i C ( t ) d t = 0 d i C ( t ) 2 d t + i C ( t ) = 0 d i C ( t ) d t i C ( t ) = − 2 Integrate both side of the above equation. ln [ i C ( t ) ] = − 2 t + c i C ( t ) = e ( − 2 t + c ) i C ( t ) = K e − 2 t The expression for the particular solution is given by, i p ( t ) = A e − 2 t cos 3 t + B e − 2 t sin 3 t ..... (3) Substitute A e − 2 t cos 3 t + B e − 2 t sin 3 t for i L ( t ) in equation (1). 2 [ A e − 2 t cos 3 t + B e − 2 t sin 3 t ] + 1 d [ A e − 2 t cos 3 t + B e − 2 t sin 3 t ] d t = 5 e − 2 t cos ( 3 t ) 2 [ A e − 2 t cos 3 t + B e − 2 t sin 3 t ] + d ( e − 2 t ( A cos 3 t + b sin 3 t ) ) d t = 5 e − 2 t cos ( 3 t ) 2 [ A e − 2 t cos 3 t + B e − 2 t s

Electrical Engineering: Principles & Applications (7th Edition)

7th Edition

ISBN: 9780134484143

Author: Allan R. Hambley

Publisher: PEARSON

See similar textbooks

Concept explainers

Time-Varying Field

Maxwell's equation in differential form are given as :

Videos

Question

Chapter 4, Problem 4.48P

To determine

The value of iL(t) for t>0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 4.47P

Chapter 4, Problem 4.49P

Students have asked these similar questions

In the circuit shown, find the following: 1) The current Ix. 2) The average power dissipated in the capacitor. 3) The total average power dissipated in the two resistors. 4) The average power of the independent voltage source and specify whether it is supplied or absorbed. 5) The total impedance seen from the terminals of the independent voltage source (Z=V/I). 20 -201 12/00V(+ 21 www 202

2- If you have a unipolar winding stepper motor, draw the driver and the control circuit. Note: The drawing is on paper.

Given the following reaction system, where Xo is the input, i.e u(t) = k₁ × Xo: $Xo -> x1; k1*Xo x2; k2*x1 x1 2 x2 ->%; k3*x2^2 x2 ->; k4*x2 Xo 1; k1 = 0.4 k2 4.5; k3 = 0.75 k4= 0.2 a) Build the model in Tellurium and run a simulation. Compute the Jacobian at steady state using the method getFull Jacobian(). Make sure you are at steady state! b) Write out the values for n and p c) Write out the differential equations. d) Write out the state space representation in terms of the rate constants etc. e) Compute the values in the Jacobian matrix from d) by substituting the values of the rate constants etc and any data you need from the simulation. f) Confirm that the Jacobian you get in e) is the same as the one computed from the simulation in a). g) Is the system stable or not? If you find an eigenvalue of zero, that means the system is marginally stable. You can get the eigenvalues using the tellurium method r.getFullEigenvalues()

Chapter 4 Solutions

Electrical Engineering: Principles & Applications (7th Edition)

Ch. 4 - Suppose we have a capacitance C discharging...Ch. 4 - The dielectric materials used in real capacitors...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - A 100F capacitance is initially charged to 1000 V....Ch. 4 - At t = 0, a charged 10{ F capacitance is connected...Ch. 4 - At time t1 , a capacitance C is charged to a...Ch. 4 - Given an initially charged capacitance that begins...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - In physics, the half-life is often used to...Ch. 4 - We know that a 50F capacitance is charged to an...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.