In the network in Fig P7.12, find i0(t) for t>0 using the differential equation approach. **Problem 7.12: Analysis Using Differential Equations**In the network shown in Figure P7.12, determine $ i_o(t) $ for $ t > 0 $ using the differential equation approach.**Figure P7.12 Explanation:**- The circuit consists of a 2 Henry inductor, a 6 Ohm resistor, a 4 Ohm resistor, a 12 Ohm resistor, and a 2 Amp current source.- The inductor is in series with the 6 Ohm resistor.- The 4 Ohm resistor is connected in parallel with the current source and the 12 Ohm resistor.- The switch is in a position such that it closes at time $ t = 0 $.- The objective is to find the current $ i_o(t) $ through the 6 Ohm resistor and inductor for $ t > 0 $.This problem involves setting up a differential equation based on the given circuit parameters and solving for the transient response of the inductor current.

Answered: Image /qna-images/answer/bc547c90-bfc7-4e0c-9285-674d746179da.jpg

Answered: In the network in Fig. P7.12, find i…

In the network in Fig. P7.12, find i (t) for t> 0 using the differential equation approach. bodom qon-d-apte 6Ω 2 H i (t) 4Ω ww = 0 fo 2 A www 312 Ω

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: The second order system response for the step input is given by 3.5 3 The damping ratio () of the…

A: Given response is -

Q: Problem 8 Find (t) for t> 0 in the network in Fig. P7.50.

A: For the given circuit the value of voltage across the 3kohms resistor needs to be calculated and the…

Q: Q3: The unit step response of a first order system reaches 10% of its final value in 2 second. What…

A: The unit step response for a first order system is given by, Final value of the response is given…

Q: P7.5.14 (Questions 4 and 5) The inductor current in the circuit shown below is given by 3+ 2e-3t A…

Q: Differential equation of a system is represented by d²y dy +5- + 115 y = 0 dt The value of damping…

A: For this problem we can easily found the value of damping ratio from standard equation.

Q: If R₂ = 2R₁ and L2 = 2L1, then the damping ratio ($) for the circuit is given by (= 3.0 (= 1.0 (=…

Q: A single loop RLC electrical circuit can be modelled as a second order system in terms of current.…

A: Taking Laplace transform of the given equation,

Q: Apply the differential equation technique to find i(t) for t>0 in the circuit shown in the figure…

A: In the given question we need to calculate the current flow through the inductor.

Q: Find the damping ratio and natural frequency for each second-order system shown below and show that…

Q: 1. You are given with two functions f(t) and h(t), as shown below. Find g(t) where g(t) = f(t)*h(t).…

A: Given

Q: An experiment was performed on your system and it was recorded that the oscillations decayed…

A: Because damping resists and thus slow the back and forth motion, the period and frequency of a…

Q: The switch in the circuit in Fig. P7.1 has been closed for a long time before opening at t = 0. a)…

A: We are authorized to answer only 3 subparts at a time since you have not mentioned which part you…

Q: Give all the steps needed to solve RL circuits using the differential equation approach

A: Find all the steps needed to solve RL circuits using differential equation approach.

Q: s + 2 T(s) s2 + 9

Q: The differential equation d²vc(t) dt² dvc(t) dt +2 + 10 vc (t) = 0 describes a second order circuit…

A: Given Data: The differential equation of a circuit is, d2 vctdt2+2 d vctdt+10 vct=0 To Find: Natural…

Q: find the differential equation that show the relationship between u(t) (input) and uR(t) (output)

A: The differential equation method is a very important approach to solve that electrical circuit that…

Q: a. Find the poles and zeros b. Find the damping ratio (C), and the natural frequency (w) c. Based on…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find i(t) and v(t) for t > O in the circuit shown. i + 3.5u(t) A (4 0.2 F 20 H V ll

Q: Using the step-by-step method, find the value of the output current, io(t), just before the switch…

A: Is = 15 mA, R1 = 3 kΩ, R2 = 4 kΩ, R3 = 4 kΩ, and R4 = 9 kΩ. Need to calculate current through the…

Q: Analyze the circuit below. Assume the circuit has reached steady state before t 0. a.) Find the…

A: In the given circuit, the current source 4ut becomes active for time t≥0 second, i.e.,…

Q: There is no energy stored in the capacitors in the circuit at the time the switch is closed. 1. a)…

A: Since we only answer up to 3 subparts, we will answer first 3. Please resubmit the question and…

Q: Which of the following represents a system with transfer function G(s)=5/(3s2 +2s+3)? a)…

A: Given:Gs=53s2+2s+3

Q: öaalg äbäi the natural response solution below is belong to a circuit * operate at i(t) = (A2 +…

A: For under damped system ,roots are imaginary. For over damped system roots are real and distinct.…

Q: 3- Find the response function c(t) for the under damping system shown in equation below, where the…

A: For the system CsRs=ωn2s2+2ζωns+ωn2 Given, the system is under damped. Input is, Rs=1s2…

Q: 7.38 Use the step-by-step method to find v(t) for t > 0 in the cir- cuit in Fig. P7.38. 18 V + 3 ΚΩ…

A: The given circuit is We need to find the voltage vo(t) for t >0 using differential equation…

Q: 10(s + 7) (s + 10)(s + 20) T(s)

Q: Use the step-by-step method to find the value of the output current just after the switch opens,…

Q: Plot the root-locus for the OLTF G(s) 10k(s+1) s2+8s+10 b/Also , calculate the gain for a damping…

Q: Use the differential equation approach to find i(t) for t>0 in the circuit in Fig. P7.14. Select the…

Q: Obtain v(t) in time domain for t>0 in the circuit below -What type of damping case does the circuit…

A: Given:A circuit, To find:a) v(t) in time domain for t>0 in the circuit.b) Type of damping case…

Q: Using the step-by-step method, find the value of the output current, io(t), just before the switch…

A: The given data is shown below:

Q: Differential equation of a system is represented by d²y dy + 100 y = 0 +11 dt The value of damping…

Q: 1. Evaluate the following integral reducing your answer to the simplest form t-3 |t-6(7+3) dr (T-)…

A: The solution is given below

Q: a) Solve the circuit in the time domain Apply the differential equation technique to find i(t) for…

A: In this question, we need to determine current i(t) as shown in the circuit.We solve this problem…

Q: 5 T(s) (s + 3)(s + 6)

Q: Calculate the damping ratio and natural frequency and determine if it is undamped, underdamped,…

A: The required parameters can be calculated by comparing the given transfer function with the general…

Q: In Figure P7.1, let G(s) = R(S) + 1350(s + 2) (s + 10) (s +32) s(s+4) (s² +8s +32) Find the…

A: In this question we need to find a steady state error of the given system for the given input.

Q: Using the step-by-step method, find the value of the output current, io(t), just before the switch…

A: The given circuit,Is=16 mA.R1=6 kΩ.R2=7 kΩ.R3=5 kΩ.R4=7 kΩ.We need to find the value of the output…

Q: 4 A 30kHz 0.⁰ R2 100 400 L1 40pH R1 260 C1 1µF

Q: 7.14 The switch in the circuit in Fig. P7.14 has been closed for a long time before opening at t =…

A: As per our policy, i have attempted one question For t = 0-, Dependent current source will be open…

Question

In the network in Fig P7.12, find i0(t) for t>0 using the differential equation approach.

**Problem 7.12: Analysis Using Differential Equations**

In the network shown in Figure P7.12, determine $ i_o(t) $ for $ t > 0 $ using the differential equation approach.

**Figure P7.12 Explanation:**

- The circuit consists of a 2 Henry inductor, a 6 Ohm resistor, a 4 Ohm resistor, a 12 Ohm resistor, and a 2 Amp current source.
- The inductor is in series with the 6 Ohm resistor.
- The 4 Ohm resistor is connected in parallel with the current source and the 12 Ohm resistor.
- The switch is in a position such that it closes at time $ t = 0 $.
- The objective is to find the current $ i_o(t) $ through the 6 Ohm resistor and inductor for $ t > 0 $.

This problem involves setting up a differential equation based on the given circuit parameters and solving for the transient response of the inductor current.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Please help me find trasform function
c) A continuous-time system is given by the differential equation, d²y(t) + 5 dt dy(t) + 6y(t) dx(t) – 4x(t) dt dt iii. Discuss the stability of the system. Justify your answer.
Solve it quickly please
Write the equation of unit step function for the figure below. g(t) 2 1 0 1 2 3 t
Control &Measurements
I need the answer as soon as possible
Question Find the damping ratio and natural frequency for each second-order system shown below and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on) predicted in that problem. T(s): 5 (s+3)(s+6)
Design RLC circuits for underdamped, overdampt and critically damped response (one circuit per response). Use Vpp < 5V, show all your calculations and simulation. Use the component values.
Write the 2nd order differential equation of v₁. What should be the value of R (R>0) for this circuit to be critically-damped? + 452 W R lemos V2 1 H
Differential equation of a system is represented by d²y dt? dy +10- + 120 y = 0 dt The value of damping ratio is:
Using the step-by-step method, find the value of the output current, io(t), just before the switch closes (at t=0-) for the network in Fig. P7.81. Given lç, 11 mA, R1 = 3 kQ, R2 = 6 kQ, R3 = 6 k0, and R4 = 7 KQ. 1 Is mA R1 ΚΩ Figure P7.81 R3 ΚΩ R2K t = 0 Los i,(1) 2 mH SR4K! Notes on entering solution: • Enter your solution in milliAmps(mA) • Enter your solution to the nearest tenth of a mA . Do not include units in your answer .ex. 5mA is entered as 5.0 2iA
= Use the differential equation approach to find i,(t) for t>0 in the circuit in Fig. P7.8.