Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 7, Problem 54P

Obtain the inductor current for both t < 0 and t > 0 in each of the circuits in Fig. 7.120.

Chapter 7, Problem 54P, Obtain the inductor current for both t  0 and t  0 in each of the circuits in Fig. 7.120.

(a)

Expert Solution
Check Mark
To determine

Calculate the value of inductor current i(t) for both t<0 and t>0 in the given circuit of Figure 7.120(a).

Answer to Problem 54P

The value of inductor current i(t) in the circuit of Figure 7.120(a) for t<0 is 1A and t>0 is 17(6+e2t)A.

Explanation of Solution

Given data:

Refer to Figure 7.120 in the textbook.

The value of inductance L in Figure 7.120(a) is 3.5H.

Formula used:

Write the general expression to find the complete response of current for the RL circuit.

i(t)=i()+[i(0)i()]etτ (1)

Here,

τ is the time constant for the RL circuit,

i(0) is the initial inductor current, and

i() is the final inductor current.

Write the expression to calculate the time constant for the RL circuit.

τ=LReq (2)

Here,

Req is the equivalent resistance of the resistor, and

L is the inductance of the inductor.

Calculation:

Figure 1 shows the modified circuit diagram when t<0.

Fundamentals of Electric Circuits, Chapter 7, Problem 54P , additional homework tip  1

In Figure 1, the switch is kept in open position for all t<0. The inductor reaches steady state and acts like a short circuit to dc. The current through the inductor i(0) is calculated by using current division rule.

i(0)=(2A)(4Ω4Ω+4Ω)=(2A)(48)=1A

Therefore, the inductor current i(t) for t<0 is 1A.

Figure 2 shows the modified circuit diagram when the switch is kept in close position for all t>0.

Fundamentals of Electric Circuits, Chapter 7, Problem 54P , additional homework tip  2

Apply Kirchhoff’s current law at node a.

2=Va4+Va12+Va42=Va(14+112+14)2=(712)Va

Rearrange the equation as follows,

Va=2(127)=247V

The final inductor current i() is calculated by using Ohm’s law.

i()=Va4Ω

Substitute 247V for Va to find the final inductor current i() in amperes.

i()=247V4Ω=24V28Ω=67A{1A=1V1Ω}

Figure 3 shows the equivalent resistance at the inductor terminal.

Fundamentals of Electric Circuits, Chapter 7, Problem 54P , additional homework tip  3

In Figure 3, the equivalent resistance is calculated as follows.

Req=(4Ω||12Ω)+4Ω=4Ω×12Ω4Ω+12Ω+4Ω=3Ω+4Ω=7Ω

Substitute 7Ω for Req and 3.5H for L in equation (2) to find the time constant τ.

τ=3.5H7Ω (3)

Substitute the units VA for Ω and VsA for H in equation (3) to find the time constant τ in seconds.

τ=3.5VsA7VA=0.5s

Substitute 67A for i(), 1A for i(0), and 0.5s for τ in equation (1) to find the current response i(t) in amperes.

i(t)=67A+[1A67A]et0.5s=67A+[17A]e2t=17(6+e2t)A

Therefore, the inductor current i(t) for t>0 is 17(6+e2t)A.

Conclusion:

Thus, the value of inductor current i(t) in the circuit of Figure 7.120(a) for t<0 is 1A and t>0 is 17(6+e2t)A.

(b)

Expert Solution
Check Mark
To determine

Calculate the value of inductor current i(t) for both t<0 and t>0 in given circuit of Figure 7.120(b).

Answer to Problem 54P

The value of inductor current i(t) in the circuit of Figure 7.120(b) for t<0 is 2A and t>0 is 3e9t4A.

Explanation of Solution

Given data:

Refer to Figure 7.120 in the textbook.

The value of inductance L in Figure 7.120(b) is 2H.

Calculation:

Figure 4 shows the modified circuit diagram when switch is kept open for a long time at t<0. The inductor reaches steady state and acts like a short circuit to dc.

Fundamentals of Electric Circuits, Chapter 7, Problem 54P , additional homework tip  4

In Figure 4, i(0) is calculated by using Kirchhoff’s voltage law.

10V=(2Ω)i(0)+(3Ω)i(0)10V=(2Ω+3Ω)i(0)10V=(5Ω)i(0)

Rearrange the equation as follows,

i(0)=10V5Ω=2A{1A=1V1Ω}

Therefore, the inductor current i(t) for t<0 is 2 A.

Figure 5 shows the redrawn circuit when switch is kept in closed position at t>0.

Fundamentals of Electric Circuits, Chapter 7, Problem 54P , additional homework tip  5

In Figure 5, apply Kirchhoff’s current law at node v.

10v2+24v6=v3102v2+246v6=v3102+246=v3+v2+v69=(13+12+16)v

Rearrange the equation as follows,

v=9(13+12+16)v=9V

The final inductor current i() is calculated by using Ohm’s law.

i()=v3Ω

Substitute 9V for v to find the final inductor current i() in amperes.

i()=9V3Ω=3A{1A=1V1Ω}

Figure 6 shows the equivalent resistance at the inductor terminal.

Fundamentals of Electric Circuits, Chapter 7, Problem 54P , additional homework tip  6

In Figure 6, the equivalent resistance is calculated as follows.

Req=(2Ω||6Ω)+3Ω=2Ω×6Ω2Ω+6Ω+3Ω=1.5Ω+3Ω=4.5Ω

Substitute 4.5Ω for Req and 2H for L in equation (2) to find the time constant τ.

τ=2H4.5Ω (4)

Substitute the units VA for Ω and VsA for H in equation (4) to find the time constant τ in seconds.

τ=2VsA4.5VA=49s

Substitute 3A for i(), 2A for i(0), and 49s for τ in equation (1) to find the current response i(t) in amperes.

i(t)=3A+[2A3A]et49s=3A+[1A]e9t4=3e9t4A

Therefore, the inductor current i(t) for t>0 is 3e9t4A.

Conclusion:

Thus, the value of inductor current i(t) in the circuit of Figure 7.120(b) for t<0 is 2A and t>0 is 3e9t4A.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
The switch in the circuit shown in Fig. 7.21 has been in position a for a longtime. At t=0, the switch moves from position a to position b. The switch is amake-before-break type; that is, the connection at position b is establishedbefore the connection at position a is broken, so the inductor current iscontinuous.5. Plot both i(t) and v(t) versus t.
The switch in the circuit shown in Fig. 7.6 has been closed for a long timebefore it is opened at t=0. Find 3. vo(t) for t≥0+,
Suppose the input to the circuit is a damped ramp of the form Kte−100t V. Find the largest value of K such that the inductor current does not exceed the 40 mA current rating

Chapter 7 Solutions

Fundamentals of Electric Circuits

Ch. 7.5 - The switch in Fig. 7.47 is closed at t = 0. Find...Ch. 7.6 - The switch in Fig. 7.52 has been closed for a long...Ch. 7.6 - Switch S1 in Fig. 7.54 is closed at t = 0, and...Ch. 7.7 - For the op amp circuit in Fig. 7.56, find vo for t...Ch. 7.7 - Find v(t) and vo(t) in the op amp circuit of Fig....Ch. 7.7 - Obtain the step response vo(t) for the circuit in...Ch. 7.8 - For the circuit in Fig. 7.66, use Pspice to find...Ch. 7.8 - The switch in Fig. 7.71 was open for a long time...Ch. 7.9 - The RC circuit in Fig. 7.74 is designed to operate...Ch. 7.9 - The flash unit of a camera has a 2-mF capacitor...Ch. 7.9 - A relay has a resistance of 200 and an inductance...Ch. 7.9 - Prob. 22PPCh. 7 - An RC circuit has R = 2 and C = 4 F. The time...Ch. 7 - The time constant for an RL circuit with R = 2 ...Ch. 7 - A capacitor in an RC circuit with R = 2 and C = 4...Ch. 7 - An RL circuit has R = 2 and L = 4 H. The time...Ch. 7 - In the circuit of Fig. 7.79, the capacitor voltage...Ch. 7 - Figure 7.79 For Review Questions 7.5 and 7.6....Ch. 7 - For the circuit in Fig. 7.80, the inductor current...Ch. 7 - Figure 7.80 For Review Questions 7.7 and 7.8....Ch. 7 - If vs changes from 2 V to 4 V at t = 0, we may...Ch. 7 - The pulse in Fig. 7.116(a) can be expressed in...Ch. 7 - In the circuit shown in Fig. 7.81...Ch. 7 - Find the time constant for the RC circuit in Fig....Ch. 7 - Determine the time constant for the circuit in...Ch. 7 - The switch in Fig. 7.84 has been in position A for...Ch. 7 - Using Fig. 7.85, design a problem to help other...Ch. 7 - The switch in Fig. 7.86 has been closed for a long...Ch. 7 - Assuming that the switch in Fig. 7.87 has been in...Ch. 7 - For the circuit in Fig. 7.88, if...Ch. 7 - The switch in Fig. 7.89 opens at t = 0. Find vo...Ch. 7 - For the circuit in Fig. 7.90, find vo(t) for t 0....Ch. 7 - For the circuit in Fig. 7.91, find io for t 0....Ch. 7 - Using Fig. 7.92, design a problem to help other...Ch. 7 - In the circuit of Fig. 7.93,...Ch. 7 - Calculate the time constant of the circuit in Fig....Ch. 7 - Find the time constant for each of the circuits in...Ch. 7 - Determine the time constant for each of the...Ch. 7 - Consider the circuit of Fig. 7.97. Find vo(t) if...Ch. 7 - For the circuit in Fig. 7.98, determine vo(t) when...Ch. 7 - In the circuit of Fig. 7.99, find i(t) for t 0 if...Ch. 7 - For the circuit in Fig. 7.100, v = 90e50t V and i...Ch. 7 - In the circuit of Fig. 7.101, find the value of R...Ch. 7 - Find i(t) and v(t) for t 0 in the circuit of Fig....Ch. 7 - Consider the circuit in Fig. 7.103. Given that...Ch. 7 - Express the following signals in terms of...Ch. 7 - Design a problem to help other students better...Ch. 7 - Express the signals in Fig. 7.104 in terms of...Ch. 7 - Express v(t) in Fig. 7.105 in terms of step...Ch. 7 - Sketch the waveform represented by i(t) = [r(t) ...Ch. 7 - Sketch the following functions: (a) x(t) = 10etu(t...Ch. 7 - Prob. 30PCh. 7 - Evaluate the following integrals: (a)e4t2(t2)dt...Ch. 7 - Prob. 32PCh. 7 - The voltage across a 10-mH inductor is 45(t 2)mV....Ch. 7 - Evaluate the following derivatives: (a) ddtut1ut+1...Ch. 7 - Find the solution to the following differential...Ch. 7 - Solve for v in the following differential...Ch. 7 - A circuit is described by 4dvdt+v=10 (a) What is...Ch. 7 - A circuit is described by didt+3i=2ut Find i(t)...Ch. 7 - Calculate the capacitor voltage for t 0 and t 0...Ch. 7 - Find the capacitor voltage for t 0 and t 0 for...Ch. 7 - Using Fig. 7.108, design a problem to help other...Ch. 7 - (a) If the switch in Fig. 7.109 has been open for...Ch. 7 - Consider the circuit in Fig. 7.110. Find i(t) for...Ch. 7 - The switch in Fig. 7.111 has been in position a...Ch. 7 - Find vo in the circuit of Fig. 7.112 when vs =...Ch. 7 - Prob. 46PCh. 7 - Determine v(t) for t 0 in the circuit of Fig....Ch. 7 - Find v(t) and i(t) in the circuit of Fig. 7.115....Ch. 7 - If the waveform in Fig. 7.116(a) is applied to the...Ch. 7 - In the circuit of Fig. 7.117, find ix for t 0....Ch. 7 - Rather than applying the shortcut technique used...Ch. 7 - Using Fig. 7.118, design a problem to help other...Ch. 7 - Determine the inductor current i(t) for both t 0...Ch. 7 - Obtain the inductor current for both t 0 and t 0...Ch. 7 - Find v(t) for t 0 and t 0 in the circuit of Fig....Ch. 7 - Prob. 56PCh. 7 - Prob. 57PCh. 7 - Rework Prob. 7.17 if i(0) = 10 A and v(t) = 20u(t)...Ch. 7 - Determine the step response vo(t) to is = 6u(t) A...Ch. 7 - Find v(t) for t 0 in the circuit of Fig. 7.125 if...Ch. 7 - In the circuit in Fig. 7.126, is changes from 5 A...Ch. 7 - For the circuit in Fig. 7.127, calculate i(t) if...Ch. 7 - Obtain v(t) and i(t) in the circuit of Fig. 7.128....Ch. 7 - Determine the value of iL(t) and the total energy...Ch. 7 - If the input pulse in Fig. 7.130(a) is applied to...Ch. 7 - Using Fig. 7.131, design a problem to help other...Ch. 7 - If v(0) = 10 V, find vo(t) for t 0 in the op amp...Ch. 7 - Prob. 68PCh. 7 - For the op amp circuit in Fig. 7.134, find vo(t)...Ch. 7 - Determine vo for t 0 when vs = 20 mV in the op...Ch. 7 - For the op amp circuit in Fig. 7.136, suppose vs =...Ch. 7 - Find io in the op amp circuit in Fig. 7.137....Ch. 7 - For the op amp circuit of Fig. 7.138, let R1 = 10...Ch. 7 - Determine vo(t) for t 0 in the circuit of Fig....Ch. 7 - In the circuit of Fig. 7.140, find vo and io,...Ch. 7 - Repeat Prob. 7.49 using PSpice or MultiSim. If the...Ch. 7 - The switch in Fig. 7.141 opens at t = 0. Use...Ch. 7 - The switch in Fig. 7.142 moves from position a to...Ch. 7 - In the circuit of Fig. 7.143, determine io(t)....Ch. 7 - In the circuit of Fig. 7.144, find the value of io...Ch. 7 - Repeat Prob. 7.65 using PSpice or MultiSim. If the...Ch. 7 - In designing a signal-switching circuit, it was...Ch. 7 - Prob. 83PCh. 7 - A capacitor with a value of 10 mF has a leakage...Ch. 7 - A simple relaxation oscillator circuit is shown in...Ch. 7 - Figure 7.146 shows a circuit for setting the...Ch. 7 - A 120-V dc generator energizes a motor whose coil...Ch. 7 - The circuit in Fig. 7.148(a) can be designed as an...Ch. 7 - An RL circuit may be used as a differentiator if...Ch. 7 - An attenuator probe employed with oscilloscopes...Ch. 7 - The circuit in Fig. 7.150 is used by a biology...Ch. 7 - To move a spot of a cathode-ray tube across the...
Knowledge Booster
Background pattern image
Electrical Engineering
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Text book image
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Text book image
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Text book image
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Text book image
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,
ENA 9.2(1)(En)(Alex) Sinusoids & Phasors - Explanation with Example 9.1 ,9.2 & PP 9.2; Author: Electrical Engineering Academy;https://www.youtube.com/watch?v=vX_LLNl-ZpU;License: Standard YouTube License, CC-BY
Electrical Engineering: Ch 10 Alternating Voltages & Phasors (8 of 82) What is a Phasor?; Author: Michel van Biezen;https://www.youtube.com/watch?v=2I1tF3ixNg0;License: Standard Youtube License