Essentials of Electrical and Computer Engineering

David V. Kerns, Jr., J. David Irwin

Chapter 15

DC Machines - all with Video Answers

Educators

Chapter Questions

Problem 1

A separately excited dc generator develops $100 \mathrm{~N}-\mathrm{m}$ of torque. Find the terminal voltage $V_a$ if $E_a=320 \mathrm{~V}, R_a=0.3 \Omega$, and $K_a \phi=$ $1.5 \mathrm{~Wb}$.

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

A separately excited dc generator develops $90 \mathrm{~N}-\mathrm{m}$ of torque and $18 \mathrm{~kW}$ of power. Compute the generator speed.

Paul Gabriel

Numerade Educator

Problem 3

A separately excited dc generator develops $100 \mathrm{~N}-\mathrm{m}$ of torque, $20 \mathrm{~kW}$ of power, and has a armature resistance of $0.25 \Omega$. If $K_a \phi=1.5 \mathrm{~Wb}$, calculate the terminal voltage.

Bruce Edelman

Numerade Educator

Problem 4

If the generator described in problem 15.2 is operated as a self-excited generator, determine the field resistance $R_f$ if the field current $I_f=3.0 \mathrm{~A}$.

Vishal Gupta

Numerade Educator

Problem 5

A sepárately excited dc generator has the following characteristics: $\tau_d=120 \mathrm{~N}-\mathrm{m}, P_d=$ $24 \mathrm{~kW}, R_a=0.12 \Omega$, and $K_a \phi=1.5 \mathrm{~Wb}$. Calculate the terminal voltage.

Bruce Edelman

Numerade Educator

Problem 6

A separately excited dc generator has a terminal voltage at no load of $360 \mathrm{~V}$ with the shaft rotating at $1600 \mathrm{rpm}$. If both $I_a$ and $I_f$ remain unchanged, what is the new terminal voltage if the shaft speed drops to $1600 \mathrm{rpm}$ ?

Bruce Edelman

Numerade Educator

Problem 7

A $300 \mathrm{~V}$ self-excited dc generator is used to supply power to a $300 \mathrm{~V}$ dc power distribution grid in an underground coal mine. Note that this application requires a constant terminal voltage of $300 \mathrm{~V}$. If the torque developed by the machine is $100.4 \mathrm{~N}-\mathrm{m}, R_a=1 \Omega$, $R_f=85 \Omega$, and $\omega=1800 \mathrm{rpm}$, find the machine's terminal output power.

Narayan Hari

Numerade Educator

Problem 8

Find the armature current in a dc shunt motor if $E_a=300 \mathrm{~V}$ and the motor develops $4 \mathrm{~kW}$ of power.

Narayan Hari

Numerade Educator

Problem 9

If $K_a \phi=1.1 \mathrm{~Wb}$, determine the speed of the motor in problem 15.8.

Narayan Hari

Numerade Educator

Problem 10

Determine the torque that is developed by the motor described in problems 15.8 and 15.9.

Narayan Hari

Numerade Educator

Problem 11

A dc shunt motor develops $30 \mathrm{~N}-\mathrm{m}$ of torque with $K_a \phi=1.4 \mathrm{~Wb}$. Find $E_a$ if $V_t=280 \mathrm{~V}$ and $R_a=0.16 \Omega$.

Narayan Hari

Numerade Educator

Problem 12

Determine the speed of the motor in problem 15.11.

Uma Kumari

Numerade Educator

Problem 13

A de shunt motor develops $30 \mathrm{hp}$ with $V_a=350 \mathrm{~V}$ and $E_a=340 \mathrm{~V}$. Find the value of the armature resistance $R_a$.

Vishal Gupta

Numerade Educator

Problem 14

If the motor in problem 15.13 operates at 1423 $\mathrm{rpm}$, find the values of $K_a \phi$ and $\tau_{d e v}$.

Narayan Hari

Numerade Educator

Problem 15

A de shunt motor has the following characteristics: $I_a=180 \mathrm{~A}, R_a=0.14 \Omega$, and $E_a=$ $340 \mathrm{~V}$. Find the terminal voltage of the motor.

Narayan Hari

Numerade Educator

Problem 16

A shunt-connected dc motor has the following characteristics: $V_t=240 \mathrm{~V}, R_a=0.22 \Omega$, and $I_a=40 \mathrm{~A}$. Determine the induced voltage.

Narayan Hari

Numerade Educator

Problem 17

Determine the armature and field currents in a dc motor if $V_t=380 \mathrm{~V}, E_a=330 \mathrm{~V}$, $R_a=0.1 \Omega$, and $R_f=120 \Omega$.

Narayan Hari

Numerade Educator

Problem 18

A separately excited dc shunt motor is operated at constant terminal voltage and constant developed power. Assuming the armature resistance is zero, if the field current (and therefore $\left.K_a \phi\right)$ is decreased, will the speed of the machine increase or decrease, and why?

Narayan Hari

Numerade Educator

Problem 19

Given the motor and operating conditions described in problem 15.18 , will the armature current increase, decrease, or remain the same, and why?

Narayan Hari

Numerade Educator

Problem 20

Find the terminal current $I_a$ in a dc shunt motor if $V_a=250 \mathrm{~V}, R_f=100 \Omega, R_a=0.1 \Omega$ $K_a \phi=1.25 \mathrm{~Wb}$, and the shaft speed is 1800 $\mathrm{rpm}$.

Narayan Hari

Numerade Educator

Problem 21

A dc shunt motor has the following characteristics: $V_a=400 \mathrm{~V}, R_f=110 \Omega$, and $R_a=$ $0.3 \Omega$. The magnetization curve for the machine running at a speed of $\omega=3476 \mathrm{rpm}$ is shown in Figure P15.21. Find the machine's armature current and developed shaft torque at $\omega=3476 \mathrm{rpm}$.
Figure P15.21 can't copy

Narayan Hari

Numerade Educator

Problem 22

Determine the input power that must be supplied to the machine in problem 15.21 .

Sheh Lit Chang

University of Washington

Problem 23

If shaft rotational losses are neglected, determine the efficiency of the dc motor described in problem 15.21.

Narayan Hari

Numerade Educator

Problem 24

A dc shunt motor has the following characteristics: $V_a=250 \mathrm{~V}, R_a=0.2 \Omega, R_f=100 \Omega$, and $\omega=1800 \mathrm{rpm}$. Use the magnetization curve in Figure P15.24 to find the torque developed by the machine.
Figure P15.24 can't copy

Narayan Hari

Numerade Educator

Problem 25

Given all the data for the machine in problem 15.24, derive a torque-speed curve for this motor and use it to find the developed torque if the shaft speed drops to $1200 \mathrm{rpm}$.

Narayan Hari

Numerade Educator

Problem 26

A shunt de motor has the following characteristics: $V_t=640 \mathrm{~V}, R_a=0.6 \Omega, R_f=120 \Omega$, and $K_a \phi=0.46 I_f$. If the motor is used to drive the wheels of a subway train, find the torque available for starting if a $20 \Omega$ resistor is connected in series with the armature.

Narayan Hari

Numerade Educator

Problem 27

A de series motor operates at full load at a speed of $640 \mathrm{rpm}$ with a terminal voltage of $280 \mathrm{~V} . E_a=236.4 \mathrm{~V}$ at a $I_t$ of $36 \mathrm{~A}$. If $R_s=0.24 \Omega$, find $R_a$. In addition, if $I_t=1.2 \mathrm{~A}$ at no load, find the no-load speed.

Narayan Hari

Numerade Educator

Problem 28

A $480 \mathrm{~V}, 120 \mathrm{hp}$ dc series motor has an armature plus field resistance of $0.12 \Omega$ and operates at $600 \mathrm{rpm}$. If the full-load current is 180 A, determine $E_a, P_d$, and $\tau_d$ at full load.

Keshav Singh

Numerade Educator

Problem 29

A $20 \mathrm{hp}, 230 \mathrm{~V}$ dc series motor draws $64 \mathrm{~A}$ when the speed is $56 \mathrm{r} / \mathrm{s}$. If $R_a=0.12 \Omega$ and $R_s=0.06 \Omega$, determine the speed when the line current is $84 \mathrm{~A}$.

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 30

A $230 \mathrm{~V}$ dc series motor draws a line current of $60 \mathrm{~A}$ when running at a rated speed of 600 rpm. $R_a=0.12 \Omega$ and $R_s=0.08 \Omega$. Determine the speed of the motor when the line current drops to $30 \mathrm{~A}$ and the no-load speed of the machine for a line current of $3.2 \mathrm{~A}$.

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