Principles and Applications of Electrical Engineering
Principles and Applications of Electrical Engineering
6th Edition
ISBN: 9780073529592
Author: Giorgio Rizzoni Professor of Mechanical Engineering, James A. Kearns Dr.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4, Problem 4.15HP

The voltage across a generic element X has the waveform shown in Figure P4.15. For 0 < t < 10 m s , determine and plot the current through X when it ¡s a:
a. 7 - Ω resistor.
b. 0.5 - μ F capacitor.
c. 7-mH inductor.

Chapter 4, Problem 4.15HP, The voltage across a generic element X has the waveform shown in Figure P4.15. For 0t10ms ,

Expert Solution
Check Mark
To determine

(a)

The current through the given element for the given voltage waveform.

To plot:

A graph of current through the element for 0<t<10ms .

Answer to Problem 4.15HP

The current through the given element for the given voltage waveform is

  iR(t)={421.571tA0<t<5ms2.1428A      5ms<t<10ms

A graph of current through the element for 0<t<10ms is shown in Figure 1.

Explanation of Solution

Given information:

Element is resistor and its value is 7Ω .

The given voltage waveform is shown below.

  Principles and Applications of Electrical Engineering, Chapter 4, Problem 4.15HP , additional homework tip  1

Calculation:

Consider the given graph for the voltage.

For 0<t<5ms, the equation of voltage will be

  v(t)0=150( 50)× 10 3(t0)v(t)=155×103tv(t)=3000t

For 5ms<t<10ms, the voltage is constant and equal to 15 V.

So, voltage can be written as

  v(t)={3000tV0<t<5ms15V         5ms<t<10ms

The given element is resistor. The current across it will be

  iR(t)=vR(t)R

Voltage vR(t) will be

  vR(t)=v(t)={3000tV0<t<5ms15V         5ms<t<10ms

For 0<t<5ms, the current will be

  iR(t)=vR(t)RiR(t)=3000t7=428.571tA

For 5ms<t<10ms, the current will be

  iR(t)=vR(t)RiR(t)=157=2.1428A

Current iR(t) will be

  iR(t)={421.571tA0<t<5ms2.1428A      5ms<t<10ms

A graph of current with respect to time is shown below.

  Principles and Applications of Electrical Engineering, Chapter 4, Problem 4.15HP , additional homework tip  2

Figure 1

Expert Solution
Check Mark
To determine

(b)

The current through the given element for the given voltage waveform.

To plot:

A graph of current through the element for 0<t<10ms .

Answer to Problem 4.15HP

The current through the given element for the given voltage waveform is

  iC(t)={1.5mA0<t<5ms0mA      5ms<t<10ms

A graph of current through the element for 0<t<10ms is shown in Figure 2.

Explanation of Solution

Given information:

Element is capacitor and its value is 0.5μF .

The given voltage waveform is shown below.

  Principles and Applications of Electrical Engineering, Chapter 4, Problem 4.15HP , additional homework tip  3

Calculation:

Consider the given graph for the voltage.

For 0<t<5ms, the equation of voltage will be

  v(t)0=150( 50)× 10 3(t0)v(t)=155×103tv(t)=3000t

For 5ms<t<10ms, the voltage is constant and equal to 15 V.

So, voltage can be written as

  v(t)={3000tV0<t<5ms15V         5ms<t<10ms

The given element is capacitor. The current across it will be

  iC(t)=Cd(vC(t))dt

Voltage vC(t) will be

  vC(t)=v(t)={3000tV0<t<5ms15V         5ms<t<10ms

For 0<t<5ms, the current will be

  iC(t)=Cd( v C ( t ))dtiC(t)=(0.5× 10 6)d( 3000t)dt=(0.5× 10 6)(3000)=1500×106A=1.5×103A=1.5mA

For 5ms<t<10ms, the current will be

  iC(t)=(0.5× 10 6)d( 15)dt=(0.5× 10 6)(0)=0mA

Current iC(t) will be

  iC(t)={1.5mA0<t<5ms0mA      5ms<t<10ms

A graph of current with respect to time is shown below.

  Principles and Applications of Electrical Engineering, Chapter 4, Problem 4.15HP , additional homework tip  4

Figure 2

Expert Solution
Check Mark
To determine

(c)

The current through the given element for the given voltage waveform.

To plot:

A graph of current through the element for 0<t<10ms .

Answer to Problem 4.15HP

The current through the given element for the given voltage waveform is

  iL(t)={5.35714A0<t<5ms16.047114A      5ms<t<10ms

A graph of current through the element for 0<t<10ms is shown in Figure 3.

Explanation of Solution

Given information:

Element is inductor and its value is 7mH .

The given voltage waveform is shown below.

  Principles and Applications of Electrical Engineering, Chapter 4, Problem 4.15HP , additional homework tip  5

Calculation:

Consider the given graph for the voltage.

For 0<t<5ms, the equation of voltage will be

  v(t)0=150( 50)× 10 3(t0)v(t)=155×103tv(t)=3000t

For 5ms<t<10ms, the voltage is constant and equal to 15 V.

So, voltage can be written as

  v(t)={3000tV0<t<5ms15V         5ms<t<10ms

The given element is inductor. The current across it will be

  iL(t)=1LtotvL(t)dt+iL(to)

Voltage vL(t) will be

  vL(t)=v(t)={3000tV0<t<5ms15V         5ms<t<10ms

For 0<t<5ms, the current will be

  iL(t)=1L t otvL(t)dt+iL( t o )iL(t)=17×10305(3000t)dt+iL(0)=1×30007×103[t22]05×103+0=1×30007×103(25× 10 62)=1×3000×25×1067×103×2=75000×10614×103=5.35714A

For 5ms<t<10ms, the current will be

  iL(t)=1L t otvL(t)dt+iL( t o )iL(t)=17×1035× 10 310× 10 3(15)dt+iL(5ms)=1×157×103[t]5×10310×103+5.35714A=1×157×103((105)×103)+5.35714A=(2.1428×103×5×103)+5.35714A=10.714+5.35714=16.07114A

Current iL(t) will be

  iL(t)={5.35714A0<t<5ms16.047114A      5ms<t<10ms

A graph of current with respect to time is shown below.

  Principles and Applications of Electrical Engineering, Chapter 4, Problem 4.15HP , additional homework tip  6

Figure 3

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Chapter 4 Solutions

Principles and Applications of Electrical Engineering

Ch. 4 - The voltage waveform shown in Figure P4.10 is...Ch. 4 - The voltage across a 0.5-mH inductor, Plotted as a...Ch. 4 - Prob. 4.13HPCh. 4 - The current through a 16-H inductor is zero at t=0...Ch. 4 - The voltage across a generic element X has the...Ch. 4 - The plots shown in Figure P4.16 are the voltage...Ch. 4 - The plots shown in Figure P4.17 are the voltage...Ch. 4 - The plots shown in Figure P4.18 are the voltage...Ch. 4 - The plots shown in Figure P4.19 are the voltage...Ch. 4 - The voltage vL(t) across a 10-mH inductor is shown...Ch. 4 - The current through a 2-H inductor is p1otted in...Ch. 4 - Prob. 4.22HPCh. 4 - Prob. 4.23HPCh. 4 - Prob. 4.24HPCh. 4 - The voltage vC(t) across a capacitor is shown in...Ch. 4 - The voltage vL(t) across an inductor is shown in...Ch. 4 - Find the average and rms values of x(t) when:...Ch. 4 - The output voltage waveform of a controlled...Ch. 4 - Refer to Problem 4.28 and find the angle + that...Ch. 4 - Find the ratio between the average and rms value...Ch. 4 - The current through a 1- resistor is shown in...Ch. 4 - Derive the ratio between the average and rms value...Ch. 4 - Find the rms value of the current waveform shown...Ch. 4 - Determine the rms (or effective) value of...Ch. 4 - Assume steady-state conditions and find the energy...Ch. 4 - Assume steady-state conditions and find the energy...Ch. 4 - Find the phasor form of the following functions:...Ch. 4 - Convert the following complex numbers to...Ch. 4 - Convert the rectangular factors to polar form and...Ch. 4 - Complete the following exercises in complex...Ch. 4 - Convert the following expressions to rectangular...Ch. 4 - Find v(t)=v1(t)+v2(t) where...Ch. 4 - The current through and the voltage across a...Ch. 4 - Express the sinusoidal waveform shown in Figure...Ch. 4 - Prob. 4.45HPCh. 4 - Convert the following pairs of voltage and current...Ch. 4 - Determine the equivalent impedance seen by the...Ch. 4 - Determine the equivalent impedance seen by the...Ch. 4 - The generalized version of Ohm’s law for impedance...Ch. 4 - Prob. 4.50HPCh. 4 - Determine the voltage v2(t) across R2 in the...Ch. 4 - Determine the frequency so that the current Ii...Ch. 4 - Prob. 4.53HPCh. 4 - Use phasor techniques to solve for the current...Ch. 4 - Use phasor techniques to solve for the voltage...Ch. 4 - Prob. 4.56HPCh. 4 - Solve for VR shown in Figure P4.57. Assume:...Ch. 4 - With reference to Problem 4.55, find the value of ...Ch. 4 - Find the current iR(t) through the resistor shown...Ch. 4 - Find vout(t) shown in Figure P4.60.Ch. 4 - Find the impedance Z shown in Figure...Ch. 4 - Find the sinusoidal steady-state output vout(t)...Ch. 4 - Determine the voltage vL(t) across the inductor...Ch. 4 - Determine the current iR(t) through the resistor...Ch. 4 - Find the frequency that causes the equivalent...Ch. 4 - a. Find the equivalent impedance Zo seen by the...Ch. 4 - A common model for a practical capacitor has...Ch. 4 - Using phasor techniques, solve for vR2 shown in...Ch. 4 - Using phasor techniques to solve for iL in the...Ch. 4 - Determine the Thévenin equivalent network seen by...Ch. 4 - Determine the Norton equivalent network seen by...Ch. 4 - Use phasor techniques to solve for iL(t) in...Ch. 4 - Use mesh analysis to determine the currents i1(t)...Ch. 4 - Prob. 4.74HPCh. 4 - Prob. 4.75HPCh. 4 - Find the Thévenin equivalent network seen by the...Ch. 4 - Prob. 4.77HPCh. 4 - Prob. 4.78HPCh. 4 - Prob. 4.79HPCh. 4 - Prob. 4.80HPCh. 4 - Use mesh analysis to find the phasor mesh current...Ch. 4 - Write the node equations required to solve for all...Ch. 4 - Determine Vo in the circuit of Figure...Ch. 4 - Prob. 4.84HP
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