Chapter 10: DC Machines

Example 1: pg 329

In [1]:
#pg 329
#calculate the emf generated
# Given data
A = 2.;# in wavewound
N = 1200.;# in rpm
phi = 0.02;# in Wb
n = 65.;# no of slots
P = 4.;
#calculations
Z = n*12;# total number of conductor
# Emf equation
Eg = (N*P*phi*Z)/(60*A);# in V
#results
print "The emf generated in V is",Eg

The emf generated in V is 624.0

Example 2: pg 329

In [2]:
#pg 329
#calculate the number of conductors
# Given data
P = 8.;
N = 1200.;# in rpm
phi = 25.;# in mWb
phi = phi * 10**-3;# in Wb
Eg = 440.;# in V
A = P;
#calculations
# Eg = (N*P*phi*Z)/(60*A);
Z = (Eg*60*A)/(phi*N*P);# in conductors
print "The numbers of conductors when armature is lap wound",Z
A = 2;
# Eg = (N*P*phi*Z)/(60*A);
Z = (Eg*60*A)/(phi*N*P);# in conductors
print "The numbers of conductors when armature is wave wound ",Z

The numbers of conductors when armature is lap wound 880.0
The numbers of conductors when armature is wave wound  220.0

Example 3: pg 330

In [3]:
#pg 330
#calculate the induced voltage
# Given data
P = 4;
phi = 20;# in mWb
phi = phi * 10**-3;# in Wb
A = 4;
P = A;
N =720.;# in rpm
n = 144.;# no of slots in slots
n1 = 2.;# no of coils 
n2 = 2;# no of turns in turns
#calculations
Z = n*n1*n2;# total number of conductor
# Generated emf
E = (N*P*phi*Z)/(60*A);# in V
#results
print "The induced voltage in V is",E

The induced voltage in V is 138.24

Example 4: pg 330

In [4]:
#pg 330
#calculate the emf
# Given data
Eg1 = 100.;# in V
phi1 = 20.;# in mWb
phi1 = phi1 * 10**-3;# in Wb
N1 = 800.;# in rpm
N2 = 1000.;# in rpm
#calculations
# Eg1/Eg2 = (phi1/phi2) * (N1/N2) but phi1 = phi2
Eg2 = (Eg1*N2)/N1;# in V
print "Part (i) : The generated emf in V is",Eg2
phi2 = 24;# in mWb
phi2 = phi2 * 10**-3;# in Wb
N2 = 900;# in rpm
# Eg1/Eg2 = (phi1/phi2) * (N1/N2) ;
Eg2 = (Eg1*N2*phi2)/(N1*phi1);# in V
print "Part (ii) : The generated emf in V is",Eg2

Part (i) : The generated emf in V is 125.0
Part (ii) : The generated emf in V is 135.0

Example 5: pg 331

In [5]:
#pg 331
#calculate the power
# Given data
P = 30;# in kW
P = P * 10**3;# in W
V = 300.;# in V
Ra = 0.05;# in ohm
Rsh = 100;# in ohm
#calculations
# p = V*I_L;
I_L = P/V;# in A
Ish = V/Rsh;# in A
Ia = I_L+Ish;# in A
Eg = V + (Ia*Ra);# in V
# power developed by armature 
power = (Eg*Ia);# in W
power = power * 10**-3;# in kW
#results
print "The total power developed by the armature in kW is",round(power,2)

The total power developed by the armature in kW is 31.43

Example 6: pg 331

In [6]:
#pg 331
#calculate the power
# Given data
V = 200;# in V
Ra = 0.5;# in ohm
Rsh = 200;# in ohm
P = 20;# in kW
P = P * 10**3;# in W
#calculations
# P = V*I_L;
I_L =P/V;# in A
Ish = V/Rsh;# in A
Ia = I_L+Ish;# in A
Eg = V + (Ia*Ra);# in V
# power developed in the armature 
power = Eg*Ia;# in W
power = power * 10**-3;# in kW
#results
print "The power developed in the armature in kW is",round(power,1)

The power developed in the armature in kW is 25.3

Example 7: pg 332

In [7]:
#pg 332
#calculate the armature current and emf
# Given data
P = 60.;
A =P;
Vbrush = 2;# in V/brush
Vt = 100.;# in V
Ra = 0.1;# in ohm
Rsh = 80;# in ohm
#calculations
Ish = Vt/Rsh;# in A
Ilamp = P/Vt;# in A
I_L = 50*Ilamp;# in A
# Armature current
Ia = I_L+Ish;# in A
# Evaluation of generated emf
Eg = Vt + (Ia*Ra) + Vbrush;# in V
#results
print "The total armature current in A is",Ia
print "The generated emf in V is",Eg

The total armature current in A is 31.25
The generated emf in V is 105.125

Example 8: pg 332

In [8]:
#pg 332
#calculate the generated voltage
# Given data
V = 440.;# in V
I_L =40.;# in A
Rse = 1.;# in ohm
Rsh = 200.;# in ohm
Ra = 0.5;# in ohm
#calculations
Ish = V/Rsh;# in A
Ia = I_L+Ish;# in A
Eg = V + (Ia*(Ra+Rse));# in V
print "The generated voltage for long shunt in V is",Eg
#Voltage across shunt field, Vsh = V + Ise*Rse = V + (I_L*Rse);
Vsh = V+(I_L*Rse);# in V
Ish = Vsh/Rsh;# in A
Ia =I_L+Ish;# in A
Eg = V + (I_L*Rse) + (Ia*Ra);# in V
print "The generated voltage for short shunt in V is",Eg

The generated voltage for long shunt in V is 503.3
The generated voltage for short shunt in V is 501.2

Example 9: pg 341

In [9]:
#pg 341
#calculate the back emf
# Given data
V = 440.;# in V
I = 80.;# in A
Rse = 0.025;# in ohm
Ra = 0.1;# in ohm
Bd = 2.;# brush drop in V
#calculations
Ia = I;# in A
Ise = I;# in A
Eb = V - (Ia*(Ra+Rse)) - Bd;# in V
#results
print "The back emf in V is",Eb

The back emf in V is 428.0

Example 10: pg 341

In [10]:
#pg 341
#calculate the armature current and back emf
# Given data
V = 250.;# in V
I_L = 20;# in A
Ra = 0.3;# in ohm
Rsh = 200;# in ohm
#calculations
Ish = V/Rsh;# in A
# I_L = Ia+Ish;
Ia = I_L-Ish;# inA
Eb = V-(Ia*Ra);# in V
#results
print "The armature current in A is",Ia
print "The back emf in V is",Eb

The armature current in A is 18.75
The back emf in V is 244.375

Example 11: pg 342

In [11]:
#pg 342
#calculate the speed in rpm
# Given data
P = 4.;
A = 2.;#(wave connected)
Z = 200.;
V=250.;# in V
phi = 25.;# in mWb
phi = phi * 10**-3;# in Wb
Ia = 60;# in A
I_L = 60;# in A
Ra = 0.15;# in ohm
Rse = 0.2;# in ohm
#calculations
#V = Eb + (Ia*Ra) + (Ia*Rse);
Eb = V - (Ia*Ra) - (Ia*Rse);# in V
# Eb = (phi*P*N*Z)/(60*A);
N = (Eb*60*A)/(phi*P*Z);# in rpm
#results
print "The speed in rpm is",N

The speed in rpm is 1374.0

Example 12: pg 343

In [12]:
#pg 343
#calculate the resistance and current
# Given data
Eb = 227.;# in V
Rsh = 160.;# in ohm
Ish = 1.5;# in A
I_L = 39.5;# in A
#calculations
V = Ish*Rsh;# in V
Ia = I_L-Ish;# in A
#V = Eb + (Ia*Ra);
Ra = (V-Eb)/Ia;# in ohm
Ia = V/Ra;# in A
#results
print "The armature resistance in ohm is",round(Ra,3)
print "The armature current in A is",round(Ia,1)

The armature resistance in ohm is 0.342
The armature current in A is 701.5

Example 13: pg 343

In [13]:
#pg 343
#calculate the ratio of speed
# Given data
V = 230;# in V
Ra = 0.115;# in ohm
Rsh = 115.;# in ohm
I_L = 100.;# inA
#calculations
Ish =V/Rsh;# in A
Ia = I_L + Ish;# in A
Eg = V + (Ia*Ra);# in V
Ia = I_L-Ish;# in A
Eb = V - (Ia*Ra);# in V
# The ratio of speed as a generator to speed as a motor 
NgBYNm = Eg/Eb;
#results
print "The ratio of speed as a generator to speed as a motor is",round(NgBYNm,3)

The ratio of speed as a generator to speed as a motor is 1.105

Example 14: pg 344

In [14]:
#pg 344
#calculate the induced voltage
# Given data
P = 4;
slots = 144.;
phi = 20.;# in mWb
phi = phi * 10**-3;# in Wb
N = 720.;# in rpm
A = 4.;
P =4.;
n1 = 2;# in coil/slot
n2 = 2;# in turns/coil
#calculations
Z = slots*n1*n2;# total number of conductor
Eg = (N*P*phi*Z)/(60*A);# in V
#results
print "The induced voltage in V is",Eg

The induced voltage in V is 138.24

Example 15: pg 344

In [15]:
#pg 344
#calculate the emf
# Given data
P = 8;
phi = 0.1;# in Wb
Z = 400.;
N =300.;# in rpm
#calculations
Eg = (N*phi*Z)/(60);# in V (A = p)
print "The emf when lap is connected in V is",Eg
# For A=2, connected armature
A = 2;
Eg = (N*phi*P*Z)/(60*A);# in V
print "The emf when wave is connected in V is",Eg

The emf when lap is connected in V is 200.0
The emf when wave is connected in V is 800.0

Example 16: pg 345

In [16]:
#pg 345
#calculate the power 
# Given data
P_L = 20;# in kW
P_L = P_L * 10**3;# in W
V = 200;# in V
Ra = 0.05;# in ohm
Rsh = 200.;# in ohm
#calculations
# P_L = V*I_L;
I_L = P_L/V;# in A
Ish = V/Rsh;# in A
Ia = I_L+Ish;# in A
Eg = V + (Ia*Ra);# in V
Pa = Eg*Ia;# in W
Pa = Pa * 10**-3;# in kW
#results
print "The power developed in armature in kW is",round(Pa,1)

The power developed in armature in kW is 20.7

Example 17: pg 345

In [17]:
#pg 345
#calculate the speed 
# Given data
N1 = 600.;# inrpm
I_L1 = 60.;# in A
V = 230.;# in V
Rsh = 115.;# in ohm
Ra= 0.2;# in ohm
Ia2 = 30.;# in A
#calculations
Ish = V/Rsh;# in A
Ia1 = I_L1 - Ish;# in A
Eb1 = V-(Ia1*Ra);# in V
Eb2 = V - (Ia2*Ra);# in V
# N1/N2 = Eb1/Eb2;
N2 = (N1*Eb2)/Eb1;# in rpm
#results
print "The speed when 30 A current through the armature in rpm is",round(N2,2)

The speed when 30 A current through the armature in rpm is 615.38

Example 18: pg 346

In [18]:
#pg 346
#calculate the speed of motor
# Given data
P = 6;
A = 6.;
Z = 500.;
Ra = 0.05;# in ohm
Rsh =25.;# in ohm
V = 100.;# in V
I_L = 120.;# in A
phi = 2*10**-2;# in Wb
#calculations
Ish = V/Rsh;# in A
Ia = I_L-Ish;# in A
Eb = V - (Ia*Ra);# in V
# Eb = (N*P*phi*Z)/(60*A);
N = (Eb*60*A)/(P*phi*Z);# in rpm
#results
print "The speed of the motor in rpm is",N

The speed of the motor in rpm is 565.2

Example 19: pg 346

In [19]:
#pg 346
#calculate the change in emf
# Given ata
N1 = 1;
N2 = 1.2*N1;
phi1 = 1;
phi2 = 0.8*phi1;
Eg1BYEg2 = (N1/N2) * (phi1/phi2);
Eg1 = 1;# assumed
# The change in emf 
#calculations
Eg2 = (Eg1*phi2*N2)/(phi1*N1);
Eg2 = Eg2 * 100;# in %
#results
print "The change in emf in percent is",Eg2

The change in emf in percent is 96.0

Example 20: pg 347

In [21]:
#pg 347
#calculate the armature power
# Given data
Pout = 25.;# in kW
Pout = Pout*10**3;# in W
Vt = 250.;# in V
Ra = 0.06;# in ohm
Rsh = 100.;# in ohm
#calculations
# Pout = Vt*I_L;
I_L = Pout/Vt;# in A
Ish = Vt/Rsh;# in A
Ia = I_L+Ish;# in A
Eg = Vt + (Ia*Ra);# in V
# Total armature power developed when working as a generator 
Pdeveloped = Eg*Ia;# in W
Pdeveloped = Pdeveloped * 10**-3;# in kW
print "Total armature power developed in kW is",round(Pdeveloped,3)
Ia = I_L-Ish;# in A
Eb = Vt - (Ia*Ra);# in V
# Total armature power developed when working as a motor 
Pdeveloped = Eb*Ia;# in W
Pdeveloped = Pdeveloped * 10**-3;# in kW
print "Total armature power developed when working as a motor in kW is",round(Pdeveloped,4)

Total armature power developed in kW is 26.255
Total armature power developed when working as a motor in kW is 23.8046

Example 21: pg 347

In [22]:
#pg 347
#calculate the useful flux
# Given data
P = 4.;
A = 4.;
Turns = 100.;
N = 600.;# in rpm
Eg = 220.;# in V
n = 2.;# no of total conductors
Z = n*Turns;
#calculations
# Eg = (N*P*phi*Z)/(60*A);
phi = (Eg*60*A)/(N*P*Z);# in Wb
print "The useful flux per mole when armature is LAP connected in Wb is",phi
A = 2;
# Eg = (N*P*phi*Z)/(60*A);
phi = (Eg*60*A)/(N*P*Z);# in Wb
print "The useful flux per mole when armature is WAVE connected in Wb is",phi

The useful flux per mole when armature is LAP connected in Wb is 0.11
The useful flux per mole when armature is WAVE connected in Wb is 0.055