Electrical Transformers and Rotating Machines
4th Edition
ISBN: 9781305494817
Author: Stephen L. Herman
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 3, Problem 10RQ
An inductor has an inductive reactance of 250 Ω when connected to a 60-Hz line. What will be the inductive reactance if the inductor is connected to a 400-Hz line?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
QUESTION 1
Consider the equations of motion of an armature controlled DC motor given by
Jw(t)+bw (t) Ki (t)
=
di (l)
L + Ri (t) + Kw (t)
=
-Tfriction - Tload (t)
Vin (t),
dt
where vin(t) is the input voltage and Tload(t) is the input load torque. The outputs are the armature current i(t) and the motor speed w(t).
When the input voltage and torque are constant, the transient response of this system has the form of the homogeneous solution.
What is the time constant of the transient response? Find the characteristic roots of this system first. Keep 3 significant figures, and do not include units. Use scientific
notation.
The constants are given below:
Nominal voltage, Vin(t) = 17 V
Moment of inertia of the rotor, J = 0.02 kg-m²
Motor viscous friction constant, b = 0.009 N-m-s
Friction torque, Tfric = 0.003 N-m
Armature inductance, L = 0.1 H
Armature resistance, R = 0.35
Back emf constant and motor torque constant, K = 0.21 N-m/A.
**Recall that the time constant (or relaxation time) is…
The following EOMS describe the behavior of an electric motor attached to a torsional spring and damper:
[Li + Rz + vb = Vin(t)
IÖ = k0b0 + T
Importantly, the equations are coupled by the fact that 7 = k₁z and v₂ = k₂0.
Here, L, R, kv, I, k, b, and kt are constants. z is the current in the motor, and is the angular displacement of the
motor (clearly then, is the motor's angular velocity). Finally, the input to the system is vin (t).
Your tasks:
A Substituting in the coupling terms (7 = k₁² and v = k„0) into the EOMs, write the state space form of the
system x = Ax + Bu, assuming your states are 2₁=2, 22 = 0, and x3 = 0. Clearly identify your matrices.
B Assume that the desired outputs of the system (to be measured) are the current z, the angle and the input
Vin all as separate elements in the vector y. Write the output equation y = Cx + Du. Hint: D will NOT be
zero in this case. Clearly identify your matrices
Assume
represen
angular velocity and 9(s) to
The following EOMS describe the behavior of an electric motor attached to a torsional spring and damper:
[Li + Rz + vb = Vin(t)
IÖ= k0b0 + T
Importantly, the equations are coupled by the fact that 7 = k₁z and v₂ = k₂0.
Here, L, R, kv, I, k, b, and kt are constants. z is the current in the motor, and is the angular displacement of the
motor (clearly then, is the motor's angular velocity). Finally, the input to the system is vin (t).
Your tasks:
A Substituting in the coupling terms (7 = ktz and v k0) into the EOMs, write the state space form of the
system x = Ax + Bu, assuming your states are x₁ = z, x₂ = 0, and x3 = 0. Clearly identify your matrices.
B Assume that the desired outputs of the system (to be measured) are the current z, the angle and the input
Vin all as separate elements in the vector y. Write the output equation y = Cx + Du. Hint: D will NOT be
zero in this case. Clearly identify your matrices
C Assume there is no stiffness to the spring (k = 0). Using w(t) to represent…
Chapter 3 Solutions
Electrical Transformers and Rotating Machines
Ch. 3 - How many degrees are the current and voltage out...Ch. 3 - How many degrees are the current and voltage out...Ch. 3 - To what is inductive reactance proportional?Ch. 3 - Four inductors, each having an inductance of 0.6...Ch. 3 - Three inductors are connected in parallel....Ch. 3 - Prob. 6RQCh. 3 - An inductor is connected to a 240-V, 1000-Hz line....Ch. 3 - Prob. 8RQCh. 3 - Prob. 9RQCh. 3 - An inductor has an inductive reactance of 250 Ω...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A centrifugal pump having four stages in parallel delivers 12 kiloLiters per minute of liquid against a head of 25m. The diameter of the impeller being 24 cm has a speed of 1800 rpm. A pump is to be made up with a'number of stages in series. In similar construction to that of the first pump to run at 1250 rpm and to deliver 15 kiloLiters/min against a total head of 250 m, find the number of stages required in this case. Select the correct response. 2. 3 7. 15 Warrow_forward1. Using Duhamel's Integral, show that the response of an undamped SDOF system subjected to step force excitation is given by the equation Po u(t) = 은 [1-cos ant] Using Duhamel's Integral, show that the response of an undamped SDOF system subjected 2. to a ramp force excitation is given by the equation sin wnt] u(t) = (Ust)o F Wntr 3. Using Duhamel's Integral, show that the response of an undamped SDOF system subjected to a step force with finite rise time excitation is given by the equation 1 u(t) = (Ust)o |1 (sin w,t – sin w, (t – t,))| Wntr Using Duhamel's Integral, show that the response of an undamped SDOF system subjected to a step force with finite rise time excitation is given by the equation 4. u(t) = (ust)o [(cos w„ (t – ta) – cos wnt)]arrow_forwardA single degree of freedom spring mass system has a natural frequency of 10 cycles per second. Another single degree of freedom spring mass system is attached to it. The latter had a natural frequency of 20 cycles/second. What is the approximate fundamental frequency of composite system?arrow_forward
- 4. Consider an undamped system, that is mx + cx + kx = f(t) with c = 0 (5= 0), with undamped period T, and f(t) such that f(t) = 1, 0 < t < (2n − 1)T/2, n an integer f(t) = 0, t≥ (2n-1)T/2 Find and plot the response for all t. The initial conditions are zero.arrow_forwardQuestion #5 Problem Statement A spring-mass damper system has the following equation of motion * + 10x + 100x = F(t) %3D where F(t) is a periodic force as shown in the figure. If the initial displacement of the mass from equilibrium position is known to be 1 mm and the mass is released from the rest then determine the total response of the system. Problem Figure F(t) (N) 2n t (s)arrow_forwardThe position with time of an object is given byx(t)=Acos(ωt) If the amplitude is 1.58 m, and the frequency is 1.2 Hz, what is the object's acceleration at 11.26 seconds?arrow_forward
- 6. Referring to Figure 5, given that the peak current Ip = 5 mA. i. Briefly explain the terms: angular velocity, frequency, and period. ii. Write the mathematical expression for the sine wave below that represent the ac current. i. Find the effective value, Ims iv. Calculate the frequency, f and the period, T v. Determine the instantaneous current at t, = 25 µs, t2 = 60 µs, t3 = 120 us i(t) 150 350 t (us) 50 250 Figure 5arrow_forward2. A spring with k = 4500 N/cm supports a mass of 1.5 Kg. Determine the 'natural frequency' of this system in rad/sec & Hz? 3. Determine the fourier series that represents the function asarrow_forwardA balanced positive-sequence wye-connected 60-Hz three-phase source has line-to-line voltages of VL = 440 V rms. This source is connected to a balanced wye-connected load. Each phase of the load consists of a 0.5-H inductance in series with a 50-? resistance. Assume that the phase of Van is zero. A) Find the line-to-neutral voltage phasor Van. Enter your answer using polar notation. Express argument in degrees. B) Find the line-to-neutral voltage phasor Vbn. Enter your answer using polar notation. Express argument in degrees. C) Find the line-to-neutral voltage phasor Vcn. Enter your answer using polar notation. Express argument in degrees. D) Find the line-to-line voltage phasor Vab. Enter your answer using polar notation. Express argument in degrees.arrow_forward
- Given the model b. For the stable case, for what values of μ is the system 1. Underdamped? 2. Overdamped? O * – (μ + 2)x + (2μ + 5)x = 0 μ = -2 or μ = -2.5 = Ο μ = 2 or μ = 2.5 = O Ο μ = -2 or μ =-5 = μ = 2. 5 or μ = -3.5 = —arrow_forwardPlease answer: How many degrees of freedom are in the system Write out the equations of morion in matrix form & Find the natural frequencies Given: k = 10 N/m; r = 0.5 m; I1 = 1.25 kg*m2 ; I2 = 1.2 kg*m2; m = 1 kgarrow_forwardQUESTION 2 Figure 2 shows a spring-mass system with m = 10 kg, k = k2= k3 = ka = 2000 N/m, ks = ko = 3000 N/m. The system driven by external forces, F = Fo sin (2xf) t, where fis the frequency in Hz. The initial displacement and initial velocity are x, and o, respectively. a) If F =0, determine the total response of the system. b) Determine the total response of the system when Fo is not equal to zero. c) If the properties of the system are to be constant, propose the value of fso that the response of the system is in phase with the external force. ki k, x (t) F=F,sin (2xf) t ks Figure 2arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Electrical Transformers and Rotating MachinesMechanical EngineeringISBN:9781305494817Author:Stephen L. HermanPublisher:Cengage Learning
Electrical Transformers and Rotating Machines
Mechanical Engineering
ISBN:9781305494817
Author:Stephen L. Herman
Publisher:Cengage Learning
Material Science, Phase Diagrams, Part 1; Author: Welt der Werkstoffe;https://www.youtube.com/watch?v=G83ZaoB3XCc;License: Standard Youtube License