# Chapter 2 - DC machines¶

## Exa:2.1 Pg No: 174¶

In [1]:
#for 50kw generator
I_1=50*1000/500 #  full load current in ampere
V_1=0.06*500 #  full load voltage drop in volts
V_1pi=V_1/I_1 #  voltage drop per ampere of current supply in volts/ampere
#for 100kw generator
I_2=100*1000/500 #  full load current in ampere
V_2=0.04*500 #  full load voltage drop in volts
V_2pi=V_2/I_2 #  voltage drop per ampere of current supply in volts/ampere
i_1=250/(1+(V_1pi/V_2pi)) #  amperes
i_2=250/(1+(V_2pi/V_1pi)) #  amperes
print '(a) Current delievered in 50kw generator = %.2f amperes'%i_1
print '    Current delievered in 100kw generator = %.2f amperes'%i_2
V_t=500-V_1pi*i_1 #  volts
print '(b) Terminal voltage = %.2f volts'%V_t

(a) Current delievered in 50kw generator = 62.50 amperes
Current delievered in 100kw generator = 187.50 amperes
(b) Terminal voltage = 481.25 volts


## Exa:2.2 Pg No: 174¶

In [2]:
from math import sqrt
E_g1=120 #  volts
E_g2=115 #  volts
R_a1=0.05 #  armature winding resistance of first generator = %.2f ohms)
R_a2=0.04 #  armature winding resistance of second generator = %.2f ohms)
R_f1=20 #  feild winding resistance of first generator = %.2f ohms)
R_f2=25 #  feild winding resistance of seccond generator = %.2f ohms)
P=25000 #  watts
V_t=(5275+sqrt((5275**2)-(4*45.09*25000)))/(2*45.09) #  terminal voltage in volts
I_1=(E_g1-(V_t*(1+(R_a1/R_f1))))/R_a1 #  amperes
I_2=(E_g2-(V_t*(1+(R_a2/R_f2))))/R_a2 #  amperes
P_1=V_t*I_1/1000 #  kilo watts
P_2=V_t*I_2/1000 #  kilo watts
print 'Power shared by generator-1 = %.2f kilo Watts'%P_1
print 'Power shared by generator-2 = %.2f kilo Watts'%P_2

Power shared by generator-1 = 17.21 kilo Watts
Power shared by generator-2 = 7.79 kilo Watts


## Exa:2.3 Pg No: 175¶

In [3]:
P=8 #  no. of poles
A=8
Phy=40*10**-3 #  flux in weber
N=500 #  speed in rpm
E_g=250 #  no-load voltage in volts
Z=(E_g*60*A)/(P*N*Phy)
print 'Number of conductors=',Z

Number of conductors= 750.0


## Exa:2.4 Pg No: 175¶

In [4]:
V_t=300 #  volts
V_b=1 #  voltage drop per brush in volts
I=200 #  amperes
R_f=200 #  shunt feild winding resistance in ohms
R_a=0.05 #  armature winding resistance in ohms
R_se=0.04 #  Series feild winding resistance in ohms
I_f=V_t/R_f #  amperes
I_a=I+I_f #  amperes
E_g=V_t+(R_a+R_se)*I_a+(2*V_b)
print 'Value of generated voltage = %.2f volts'%E_g
print 'Value of armature current = %.2f Ampers'%I_a

Value of generated voltage = 320.09 volts
Value of armature current = 201.00 Ampers


## Exa:2.5 Pg No: 175¶

In [1]:
V_t=250 #  volts
I=195 #  amperes
R_f=50 #  shunt feild winding resistance in ohms
R_a=0.05 #  armature winding resistance in ohms
I_f=V_t/R_f #  amperes
I_a=I+I_f #  amperes
E_g=V_t+(R_a*I_a)
R_L=V_t/I
print '(a) Value of shunt feild current = %.2f Amperes'%I_f
print '(b) Value of armature current = %.2f Amperes'%I_a
print '(c) Value of generated voltage = %.2f volts'%E_g
print '(d) Value of load resistance = %.2f ohms'%R_L

(a) Value of shunt feild current = 5.00 Amperes
(b) Value of armature current = 200.00 Amperes
(c) Value of generated voltage = 260.00 volts
(d) Value of load resistance = 1.00 ohms


## Exa:2.6 Pg No: 176¶

In [2]:
V_t=250 #  volts
V_AC=V_t
V_b=1 #  voltage drop per brush in volts
I=40 #  amperes
R_f=100 #  shunt feild winding resistance in ohms
R_a=0.05 #  armature winding resistance in ohms
R_se=0.04 #  series feild winding resistance in ohms
V_BC=V_AC+I*R_se #  volts
I_f=V_BC/R_f #  amperes
I_a=I+I_f #  amperes
E_g=V_BC+(R_a*I_a)*(2*V_b)
print ' Value of armature current = %.2f Amperes'%I_a
print ' Value of generated voltage = %.2f volts'%E_g

 Value of armature current = 42.52 Amperes
Value of generated voltage = 255.85 volts


## Exa:2.7 Pg No: 177¶

In [3]:
P=8 #  no. of poles
A=8
Z=760 #  no.of conductors
Phy=35*10**-3 #  flux in weber
N=500 #  speed in rpm
E_g=(P*N*Phy*Z)/(60*A)
print 'Value of generated emf = %.2f volts'%E_g

Value of generated emf = 221.67 volts


## Exa:2.8 Pg No: 178¶

In [5]:
from math import pi
P=8 #  no. of poles
S=70 #  no. of slots
C=22 #  conductors per slot
A=8
D=0.48 #  meter
Z=S*C #  no.of conductors
r=0.64 #  ratio of pole arc to pole pitch
l=0.28 #  length of pole shoe in meter
B=0.32 #  air gap flux density in weber/meter**2
E_g=400 #  volts
Pole_arc=r*pi*D/P #  meter
Ao=Pole_arc*l #  Area of pole shoe in meter
Phy=Ao*B #  weber
N=E_g*60*A/(Phy*Z*P)
print 'Speed of generator = %.2f rpm'%N

Speed of generator = 1441.79 rpm


## Exa:2.9 Pg No: 179¶

In [1]:
V_t=200 #  volts
P=4 #  no. of poles
A=2
Z=676 #  no.of conductors
R_L=10 #  load resistance in ohms
R_a=0.34 #  armature winding resistance in ohms
R_f=100 #  feild winding resistance in ohms
N=600 #  speed in rpm
I_f=V_t/R_f #  amperes
I=V_t/R_L #  amperes
I_a=I+I_f
E_g=V_t+I_a*R_a
Phy=E_g*60*A/(P*N*Z)
print '(a) Armature current = %.2f amperes'%I_a
print '(b) Generated emf = %.2f volts'%E_g
print '(c) flux/pole = %.2f mili weber'%(Phy*1000)

(a) Armature current = 22.00 amperes
(b) Generated emf = 207.48 volts
(c) flux/pole = 15.35 mili weber


## Exa:2.10 Pg No: 180¶

In [2]:
V_t=250 #  volts
P=6 #  no. of poles
A=P
Z=700 #  no.of conductors
R_a=0.04 #  armature winding resistance in ohms
R_f=100 #  feild winding resistance in ohms
N=1000 #  speed in rpm
I_f=V_t/R_f #  amperes
I_a=7.2/R_a #  amperes
I=I_a-I_f #  amperes
E_g=V_t+I_a*R_a
Phy=E_g*60*A/(P*N*Z)
print '(a) Load current = %.2f amperes'%I
print '(b) Generated emf = %.2f volts'%E_g
print '(c) flux/pole = %.2f mili weber'%(Phy*1000)

(a) Load current = 178.00 amperes
(b) Generated emf = 257.20 volts
(c) flux/pole = 22.05 mili weber


## Exa:2.11 Pg No: 182¶

In [4]:
P_o=22000 #  power in watts
V_t=220 #  volts
V_b=1 #  per brush drop in volts
P=4 #  no. of poles
A=2
R_se=0.04 #  series resistance in ohms
R_a=0.05 #  armature winding resistance in ohms
R_f=110 #  feild winding resistance in ohms
Phy=7.8*10**-3 #  weber
N=1000 #  speed in rpm
I=P_o/V_t #  amperes
I_f=V_t/R_f #  amperes
I_a=I+I_f
E_g=V_t+I_a*(R_a+R_se)+2*V_b
Z=E_g*60*A/(Phy*N*P)
print '(a) Armature current = %.2f amperes'%I_a
print '(b) Generated emf = %.2f volts'%E_g
print '(c) No. of conductors of armature= %.2f'%Z

(a) Armature current = 102.00 amperes
(b) Generated emf = 231.18 volts
(c) No. of conductors of armature= 889.15


## Exa:2.12 Pg No: 182¶

In [5]:
P=6 #  no. of poles
A=2
Z=350 #  no. of conductors
R_a=0.8 #  armature winding resistance in ohms
R_f=120 #  feild winding resistance in ohms
Phy=0.02 #  weber
N=1000 #  speed in rpm
R_L=12 #  load resistance in ohms
E_g=Phy*N*Z*P/(60*A) #  emf induced in volts
V_t=E_g/(1+((1/R_f)+(1/R_L))*R_a)
I_L=V_t/R_L #  amperes
P_o=V_t*I_L #  watts
print 'Power absorbed by the load = %.2f watts'%P_o

Power absorbed by the load = 10208.33 watts


## Exa:2.13 Pg No: 182¶

In [6]:
P1=200*10**3 #  initial load in watts
P2=125*10**3 #  final load in watts
V_t=250 #  volts
V_b=2 #  total brush drop in volts
P=6 #  no. of poles
R_a=0.015 #  armature winding resistance in ohms
I_g1=P1/V_t #  amperes
I_a1=I_g1 #  amperes
E_g1=V_t+I_a1*R_a+V_b #  volts
I_g2=P2/V_t #  amperes
I_a2=I_g2 #  amperes
E_g2=V_t+I_a2*R_a+V_b #  volts
#since E_g is directly proportional to N
#therefore,E_g1/E_g2=N_1/N_2
r=E_g2/E_g1
reduction=(1-r)*100
print 'Percentage reduction in speed = %.2f %%'%reduction

Percentage reduction in speed = 1.70 %


## Exa:2.14 Pg No: 183¶

In [7]:
from math import ceil
V_t=400 #  volts
V_b=2 #  total brush drop in volts
R_a=0.12 #  armature winding resistance in ohms
N1=1000 #  speed in rpm
I_a1=150 #  amperes
I_a2=100 #  amperes
R_L=V_t/I_a1 #  load resistance in ohms
E_g1=V_t+I_a1*R_a+V_b #  volts
V_to=R_L*I_a2 #  volts
E_g2=ceil (V_to+I_a2*R_a+V_b) #  volts
#Since E_g is directly proportional to N
#therefore,E_g1/E_g2=N1/N2
N2= N1*E_g2/E_g1 #  rpm
print 'Speed = %.2f rpm'%(ceil(N2))

Speed = 510.00 rpm


## Exa:2.15 Pg No: 184¶

In [2]:
from math import pi
P_o=25000 #  output power in watts
V_t=250 #  volts
R_se=0.05 #  series resistance in ohms
R_a=0.04 #  armature winding resistance in ohms
R_f=50 #  shunt feild winding resistance in ohms
Eff=0.89 #  efficiency
N=1000 #  speed in rpm
I=P_o/V_t #  amperes
I_f=V_t/R_f #  amperes
I_a=I+I_f
P_cu=R_a*I_a**2+R_se*I_a**2+R_f*I_f**2 #  copper loss in watts
print '(a) Cu-loss = %.2f watts'%P_cu
P_i=P_o/Eff #  input power in watts
P_L=P_i-P_o #  total losses in watts
P_fric=P_L-P_cu
print '(b) Iron and friction loss = %.2f watts'%P_fric
T=P_i*60/(2*pi*N)
print '(c) Torque = %.2f N-m'%T

(a) Cu-loss = 2242.25 watts
(b) Iron and friction loss = 847.64 watts
(c) Torque = 268.24 N-m


## Exa:2.16 Pg No: 184¶

In [2]:
from math import pi,ceil
I_a=50 #  amperes
P=6 #  no.of poles
E_g=200 #  volts
N=1500 #  speed in rpm
A=6
L=0.25 #  meter
d=0.2 #  meter
B=0.9 #  tesla
Theta=360/P #  angle subtended by pole shoe in degrees
l=pi*L*Theta/360 #  arc length of pole shoe in meter
area=l*d #  meter**2
Phy=B*area
print '(a) Flux per pole = %.2f Weber'%Phy
Z=ceil(E_g*60/(Phy*N))
print '(b) Total no. of conductors=%.2f'%Z
T=9.55*E_g*I_a/N
print '(c) Torque = %.2f Newton-meter'%T

(a) Flux per pole = 0.02 Weber
(b) Total no. of conductors=340.00
(c) Torque = 63.67 Newton-meter


## Exa:2.17 Pg No: 185¶

In [1]:
P=40000 #  watts
E_g=400 #  volts
A=4
Pole=4
Z=2*30*12 #  no. of conductors
theta_m=10 #  degrees
I_a=P/E_g #  armature current in amperes
I=I_a/A #  current in each conductor in amperes
AT_d=Z*I*theta_m/360
print '(a) Demagnetizing Ampere Turns per pole=%.2f'%AT_d
AT_cm=Z*I*((1/(2*Pole))-(theta_m/360))
print '(b) Cross magnetizing Ampere Turns per pole=%.2f'%AT_cm
n=Z*I*0.8/(2*Pole*100)
print '(c) Number of turns per pole=%.2f'%n

(a) Demagnetizing Ampere Turns per pole=500.00
(b) Cross magnetizing Ampere Turns per pole=0.00
(c) Number of turns per pole=18.00


## Exa:2.18 Pg No: 185¶

In [2]:
V_t1=280 #  terminal voltage of generator-1 in volts
V_nl1=240 #  no-load voltage of generator-1 in volts
V_t2=300 #  terminal voltage of generator-2 in volts
V_nl2=240 #  no-load voltage of generator-2 in volts
I_s1=40 #  supply current to generator-1 in amperes
I_s2=50 #  supply current to generator-2 in amperes
V_d1=V_t1-V_nl1 #  voltage drop for generator-1 in volts
V_d2=V_t2-V_nl2 #  voltage drop for generator-2 in volts
V_d1_pa=V_d1/I_s1 #  voltage drop per ampere for generator-1 in volts/ampere
V_d2_pa=V_d2/I_s2 #  voltage drop per ampere for generator-2 in volts/ampere
I_2=(20+60)/(V_d1_pa+V_d2_pa) #  amperes
I_1=60-I_2 #  amperes
print '(a) Current supplied by generator-1 = %.2f amperes'%I_1
print '    Current supplied by generator-2 = %.2f amperes'%I_2
V_1=V_t1-(V_d1_pa*I_1) #  volts
V_2=V_t2-(V_d2_pa*I_2) #  volts
print '(b) Output voltage of generator-1 = %.2f volts'%V_1
print '(b) Output voltage of generator-2 = %.2f volts'%V_2
P_1=V_1*I_1/1000 #  kilo watts
P_2=V_2*I_2/1000 #  kilo watts
print '(c) Output KW of generator-1 = %.2f kilo watts'%P_1
print '(c) Output KW of generator-2 = %.2f kilo watts'%P_2

(a) Current supplied by generator-1 = 20.00 amperes
Current supplied by generator-2 = 40.00 amperes
(b) Output voltage of generator-1 = 260.00 volts
(b) Output voltage of generator-2 = 260.00 volts
(c) Output KW of generator-1 = 5.00 kilo watts
(c) Output KW of generator-2 = 10.00 kilo watts


## Exa:2.19 Pg No: 186¶

In [3]:
V=250 #  volts
I_L=80 #  amperes
R_a=0.12 #  ohms
R=100 #  ohms
I_f=V/R #  amperes
I_a1=I_L+I_f #  amperes (generator)
E_1=V+(I_a1*R_a) #  volts (generator)
I_a2=I_L-I_f #  amperes (motor)
E_2=V-(I_a2*R_a) #  volts (motor)
Ratio=E_1/E_2
print 'Ratio of speed as a generator to speed as motor=%.2f'%Ratio

Ratio of speed as a generator to speed as motor=1.08


## Exa:2.20 Pg No: 186¶

In [4]:
V=200 #  volts
I_a0=2 #  amperes
R_a=0.4 #  ohms
I_a1=50 #  amperes
N_1=1200 #  rpm
E_0=V-(I_a0*R_a) #  volts
E_1=V-(I_a1*R_a) #  volts
N_0=N_1*(E_0/E_1) #  rpm
print 'No-load speed = %.2f rpm'%N_0

No-load speed = 1328.00 rpm


## Exa:2.21 Pg No: 187¶

In [5]:
V=250 #  volts
I_L1=5 #  amperes
R_a=0.2 #  ohms
R_f=250 #  ohms
I_f=V/R_f #  amperes
I_a1=I_L1-I_f #  amperes
I_L2=50 #  amperes
I_a2=I_L2-I_f #  amperes
N_1=1000 #  rpm
E_2=V-(I_a2*R_a) #  volts
E_1=V-(I_a1*R_a) #  volts
N_2=N_1*(E_2/E_1) #  rpm
print 'speed of motor = %.2f rpm'%N_2

speed of motor = 963.88 rpm


## Exa:2.22 Pg No: 187¶

In [6]:
V=250 #  volts
P_i=50*10**3 #  watts
I_L1=P_i/V #  amperes
R_a=0.02 #  ohms
R_f=50 #  ohms
I_f=V/R_f #  amperes
I_a1=I_L1+I_f #  amperes
I_L2=P_i/V #  amperes
I_a2=I_L2-I_f #  amperes
N_1=400 #  rpm
E_2=V-(I_a2*R_a)-(2*1) #  volts
E_1=V+(I_a1*R_a)+(2*1) #  volts
N_2=int(N_1*(E_2/E_1)) #  rpm
print 'speed of motor = %.2f rpm'%N_2

speed of motor = 381.00 rpm


## Exa:2.23 Pg No: 188¶

In [9]:
from math import pi
P=4 #  no of poles
Z=560 #  no of conductors
A=2
V=250 #  volts
P_o=10*10**3 #  watts
R_a=0.2 #  ohms
I_f=1 #  amperes
I_a=60 #  amperes
N=1000 #  rpm
V_b=1*2#in volts
E=V-(I_a*R_a)-V_b #  volts
T=60*E*I_a/(2*pi*N) #  Newton-meter
print '(a) Total torque = %.2f Newton-meter'%T
T_useful=P_o*60/(2*pi*N)
print '(b) Useful torque = %.2f Newton-meter'%T_useful
Phy=60*E*A/(N*P*Z)
print '(c) Useful flux per pole = %.2f Weber'%Phy
P_d=(V*I_a)-((I_a**2)*R_a)-(V_b*I_a) #  Watts
P_rot=P_d-P_o
print '(d) Rotational losses = %.2f Watts'%P_rot
P_i=V*(I_a+I_f) #  Watts
Eff=P_o*100/P_i
print '(e) Efficiency = %.2f %%'%Eff

(a) Total torque = 135.22 Newton-meter
(b) Useful torque = 95.49 Newton-meter
(c) Useful flux per pole = 0.01 Weber
(d) Rotational losses = 4160.00 Watts
(e) Efficiency = 65.00 %


## Exa:2.24 Pg No: 189¶

In [10]:
V=460 #  volts
R_a=0.8 #  ohms
I_a1=40 #  amperes
I_a2=30 #  amperes
N_1=500 #  rpm
E_1=V-(I_a1*R_a) #  volts
E_2=V-(I_a2*R_a) #  volts
N_2=int(E_2*I_a1*N_1/(E_1*I_a2))
print 'Speed = %.2f rpm'%N_2
ratio=(I_a2/I_a1)**2
T_c=(1-ratio)*100
print 'Percentage change in torque=%.2f'%T_c

Speed = 679.00 rpm
Percentage change in torque=100.00


## Exa:2.25 Pg No: 190¶

In [13]:
from math import sqrt
V=220 #  volts
R_a=0.1 #  ohms
I_a1=100 #  amperes
I_a2=sqrt(I_a1**2/2) #  amperes
N_1=800 #  rpm
E_1=V-(I_a1*R_a) #  volts
E_2=V-(I_a2*R_a) #  volts
N_2=int(E_2*I_a1*N_1/(E_1*I_a2))
print 'Speed = %.2f rpm'%N_2

Speed = 1147.00 rpm


## Exa:2.26 Pg No: 192¶

In [1]:
V=250 #  volts
R_a=0.25 #  ohms
I_a1=50 #  amperes
I_a2=I_a1/0.9 #  amperes
N_1=750 #  rpm
E_1=V-(I_a1*R_a) #  volts
E_2=V-(I_a2*R_a) #  volts
N_2=int(E_2*N_1/(E_1*0.9))
print 'Speed = %.2f rpm'%N_2

Speed = 828.00 rpm


## Exa:2.27 Pg No: 192¶

In [2]:
V=120 #  volts
V_b=3 #  volts
R_a=0.2 #  ohms
R_f=60 #  ohms
I_L1=40 #  amperes
I_f=V/R_f #  inn amperes
I_a1=I_L1-I_f #  amperes
N_1=1800 #  rpm
E_1=V-(I_a1*R_a)-V_b #  volts
I_L2=I_L1/2
I_a2=I_L2-I_f
E_2=V-(I_a2*R_a)-V_b #  volts
N_2=int(E_2*N_1/E_1)
print '(a) Speed at half load = %d rpm'%N_2
I_L3=I_L1*1.25
I_a3=I_L3-I_f
E_3=V-(I_a3*R_a)-V_b #  volts
N_3=int(E_3*N_1/E_1)
print '(b) Speed at 125%% load = %d rpm'%N_3

(a) Speed at half load = 1865 rpm
(b) Speed at 125% load = 1767 rpm


## Exa:2.28 Pg No: 192¶

In [4]:
V=220 #  volts
R_a=0.1 #  ohms
N_1=800 #  rpm
N_2=520 #  rpm
I_a1=20 #  ampers
E_1=V-(I_a1*R_a) #  volts
E_2=N_2*E_1/N_1 #  volts
R_A=-(E_2-V+I_a1*R_a)/20
print 'Additional resistance = %.2f ohms'%R_A

Additional resistance = 3.82 ohms


## Exa:2.29 Pg No: 193¶

In [5]:
V=240 #  volts
R_a=0.3 #  ohms
N_1=1500 #  rpm
I_a=40 #  ampers
E=V-(I_a*R_a) #  volts
R_1=(V-I_a*R_a)/I_a
print '(a) Additional resistance at starting = %.2f ohms'%R_1
N_2=1000 #  rpm
E_2=N_2*E/N_1 #  volts
R_2=-(E_2-V+I_a*R_a)/I_a
print '(b) Additional resistance at 1000 rpm = %.2f ohms'%R_2

(a) Additional resistance at starting = 5.70 ohms
(b) Additional resistance at 1000 rpm = 1.90 ohms


## Exa:2.30 Pg No: 194¶

In [6]:
V=250 #  volts
R_a=0.2 #  ohms
N_1=800 #  rpm
R_f=250 #  ohms
I_f=V/R_f #  amperes
I=41 #  ampers
I_a1=I-I_f #  amperes
E_1=V-(I_a1*R_a) #  volts
E_2=V-(I_a1*(R_a+2)) #  volts
N_2=E_2*N_1/E_1
print '(a) Speed at full load = %.2f rpm'%N_2
I_a2=I_a1*2 #  amperes
E_3=V-I_a2*(R_a+2) #  volts
N_3=E_3*N_1/E_1 #  rpm
print '(b) Speed at double full load = %.2f rpm'%N_3
I_ao=V/(R_a+2)
r=I_ao/I_a1
print '(c) stalling torque is %.2f times full load torque'%r

(a) Speed at full load = 535.54 rpm
(b) Speed at double full load = 244.63 rpm
(c) stalling torque is 2.84 times full load torque


## Exa:2.31 Pg No: 194¶

In [7]:
V=200 #  volts
R_a=0.4 #  ohms
N_1=1000 #  rpm
N_2=800 #  rpm
I_a1=20 #  amperes
E_1=V-(I_a1*R_a) #  volts
I_a2=0.8*I_a1 #  amperes
E_2=N_2*I_a2*E_1/(N_1*I_a1) #  volts
R=-(E_2-193.6)/16
print 'the resistance to be inserted in series = %.2f ohms'%R

the resistance to be inserted in series = 4.42 ohms


## Exa:2.32 Pg No: 195¶

In [9]:
from math import sqrt
V=500 #  volts
R_a=0.5 #  ohms
I_a1=60 #  amperes
E_1=V-(I_a1*R_a) #  volts
I_a2=sqrt(((0.75)**3)*I_a1**2) #  amperes
E_2=0.75*E_1*I_a2/I_a1 #  volts
R=-(E_2-480.5)/38.97
print 'the resistance to be inserted in series = %.2f ohms'%R

the resistance to be inserted in series = 6.45 ohms


## Exa:2.33 Pg No: 196¶

In [4]:
V=500 #  volts
R_a=0.2 #  ohms
I_o=4 #  amperes
I_f=1 #  amperes
P_c=V*I_o-(((I_o-I_f)**2)*R_a) #  watts
I_1=20 #  /in amperes
P_i1=V*I_1 #  watts
P_a1=((I_1-I_f)**2)*R_a #  watts
P_L1=P_c+P_a1 #  watts
P_o1=P_i1-P_L1 #  watts
print '(a) Output = %.2f watts'%P_o1
print '  Efficiency = %.2f %%'%(P_o1/P_i1*100)
I_2=100 #  /in amperes
P_i2=V*I_2 #  watts
P_a2=((I_2-I_f)**2)*R_a #  watts
P_L2=P_c+P_a2 #  watts
P_o2=P_i2-P_L2 #  watts
print '(b) Output = %.2f watts'%P_o2
print '  Efficiency = %.2f %%'%(P_o2/P_i2*100)

(a) Output = 7929.60 watts
Efficiency = 79.30 %
(b) Output = 46041.60 watts
Efficiency = 92.08 %


## Exa:2.34 Pg No: 196¶

In [5]:
V=240 #  volts
V_b=2 #  volts
R_a=0.15 #  ohms
P=4
Z=700
Phy=0.06 #  Webers
A=P
I_o=7 #  amperes
I_f=2 #  amperes
I=90 #  amperes
I_ao=I_o-I_f #  amperes
E_bo=V-I_ao*R_a-V_b #  volts
N_o=E_bo*60*A/(P*Phy*Z) #  rpm
print '(a)no load speed = %.2f rpm'%N_o
I_a=I-I_f #  amperes
E_b1=V-I_a*R_a-V_b #  volts
N=E_b1*N_o/(E_bo*0.98)
print '(b)Full load speed = %.2f rpm'%N
SR=100*(N_o-N)/N
print '(c)Speed Regulation = %.2f %%'%SR

(a)no load speed = 338.93 rpm
(b)Full load speed = 327.70 rpm
(c)Speed Regulation = 3.43 %


## Exa:2.35 Pg No: 197¶

In [6]:
V=220 #  volts
V_b=1 #  volts
R_f=110 #  ohms
R_a=0.14 #  ohms
I_o=7 #  amperes
I_f=2 #  amperes
I=90 #  amperes
N_1=700 #  rpm
I_ao=I_o-I_f #  amperes
E_bo=V-I_ao*R_a-V_b #  volts
I=55 #  amperes
I_a1=I-I_f #  amperes
E_b1=V-I_a1*R_a-V_b #  volts
N_o=E_bo*N_1/E_b1
print '(a)no load speed = %.2f rpm'%N_o
I_a2=35 #  amperes
N_2=900 #  rpm
E_b2=V-I_a2*R_a-V_b #  volts
Phy_r=E_b2*N_1/(E_b1*N_2)
R=(1-Phy_r)*100
print '(b)Percentage reduction in flux per pole = %.2f %%'%R

(a)no load speed = 722.23 rpm
(b)Percentage reduction in flux per pole = 21.30 %


## Exa:2.36 Pg No: 198¶

In [7]:
V=240 #  volts
R_f=120 #  ohms
R_a=0.25 #  ohms
I_1=60 #  amperes
I_f=V/R_f #  amperes
I_a1=I_1-I_f #  amperes
E_b1=V-I_a1*R_a #  volts
N_o=1000 #  rpm
I=6 #  amperes
I_ao=I-I_f #  amperes
E_bo=V-I_ao*R_a #  volts
N_1=N_o*E_b1/E_bo
print '(a)Full load speed = %.2f rpm'%N_1
SR=100*(N_o-N_1)/N_o
print '(b)Speed regulation = %.2f %%'%SR
P_o=E_b1*I_a1-(E_bo*I_ao)
HP=P_o/746
print '(c)HP rating = %.2f HP'%HP
P_i=V*I_1
Eff=P_o*100/P_i
print '(d)Efficiency = %.2f %%'%Eff

(a)Full load speed = 943.51 rpm
(b)Speed regulation = 5.65 %
(c)HP rating = 16.25 HP
(d)Efficiency = 84.19 %


## Exa:2.37 Pg No: 199¶

In [8]:
V=240 #  volts
P=4
Phy=0.008 #  webers
Z=1000
A=2
R_f=240 #  ohms
R_a=0.4 #  ohms
I_1=25 #  amperes
I_f=V/R_f #  amperes
I_a1=I_1-I_f #  amperes
E_b=V-I_a1*R_a #  volts
N=E_b*60*A/(P*Z*Phy)
print '(a)speed = %.2f rpm'%N
P_m=E_b*I_a1
T_g=(9.55*P_m)/N
print '(b)Torque = %.2f N-m'%T_g
P_f=P_m-800
P_i=V*I_1
Eff=P_f*100/P_i
print '(c)Efficiency = %.2f %%'%Eff

(a)speed = 864.00 rpm
(b)Torque = 61.12 N-m
(c)Efficiency = 78.83 %


## Exa:2.38 Pg No: 201¶

In [9]:
P_out=20000 #  watts
P_in=23000 #  watts
V=250 #  volts
R_f=125 #  ohms
R_a=0.2 #  ohms
I_L=P_in/V #  amperes
I_f=V/R_f #  amperes
I_a1=I_L-I_f #  amperes
P_cu=(I_a1**2)*R_a
P_fcu=V*I_f
P_tcu=P_cu+P_fcu
P_fric=P_in-P_out-P_tcu
P_o=12000 #  watts
P_m=P_o+P_fric
I_a2=53.85
P_tcu2=((I_a2**2)*R_a)+250
P_in_2=P_m+P_tcu2
print 'Power input = %.2f watts'%P_in_2
Eff=P_o*100/P_in_2
print 'Efficiency = %.2f %%'%Eff

Power input = 13709.96 watts
Efficiency = 87.53 %


## Exa:2.39 Pg No: 202¶

In [11]:
from math import sqrt
V=240 #  volts
R_f=240 #  ohms
R_a=0.6 #  ohms
I_o=5 #  amperes
I=18 #  amperes
I_f=V/R_f #  amperes
I_ao=I_o-I_f
I_a1=I-I_f
E_bo=V-I_ao*R_a #  volts
E_b1=V-I_a1*R_a #  volts
P_dnL=E_bo*I_ao #  watts
P_m=E_b1*I_a1 #  watts
P_o=P_m-P_dnL
P_i=V*I #  watts
Eff=P_o/P_i
print '(a)Efficiency = %.2f %%'%(Eff*100)
I_a=sqrt((P_dnL+V*1)/R_a)
print '(b)Armature current = %.2f Amperes'%I_a
E_b=V-I_a*R_a
P_m2=E_b*I_a #  watts
P_out=P_m2-P_dnL #  watts
P_in=V*I_a #  watts
Eff_m=P_out/P_in
print '(c)Max Efficiency = %.2f %%'%(Eff_m*100)

(a)Efficiency = 68.43 %
(b)Armature current = 44.54 Amperes
(c)Max Efficiency = 79.97 %


## Exa:2.40 Pg No: 202¶

In [1]:
V=230 #  volts
R_a=0.4 #  ohms
I_a1=3.4 #  amperes
R_f=170 #  ohms
E_b1=V-I_a1*R_a
I_f=V/R_f
I_L=41 #  amperes
I_a2=I_L-I_f
E_b2=214.142 #  volts
N_1=1000 #  rpm
N_2=N_1*E_b2/(E_b1*0.96) #  rpm
print '(a)Speed at full load = %.2f rpm'%N_2
T_a=9.55*E_b2*I_a2/N_2
print 'Torque Developed = %.2f N-m'%T_a
P_r=E_b1*I_a1
P_m=E_b2*I_a2
P_f=P_m-P_r
print '(b)Shaft Power = %.2f watts'%P_f
P_in=V*I_L
Eff=P_f/P_in
print '(c)Efficiency = %.2f %%'%(Eff*100)

(a)Speed at full load = 975.61 rpm
Torque Developed = 83.85 N-m
(b)Shaft Power = 7788.30 watts
(c)Efficiency = 82.59 %


## Exa:2.41 Pg No: 203¶

In [3]:
V=240 #  volts
R_a=0.25 #  ohms
R_f=120 #  ohms
I_f=V/R_f
I_L=26.0 #  amperes
I_a=I_L-I_f
N_1=1000.0 #  rpm
N_2=900.0 #  rpm
E_b1=V-I_a*R_a
r=N_1/N_2
R=(E_b1-(E_b1/r))/I_a
print '(a)Value of external resistance when the load torque is independent of speed = %.2f ohms'%R
I_a2=I_a/r
R1=(E_b1-(E_b1/r))/I_a2
print '(b)Value of external resistance when the load torque is proportional to speed = %.2f ohms'%R1
I_a2_n=I_a/r**2
R2=(E_b1-(E_b1/r))/I_a2_n
print '(a)Value of external resistance when the load torque is independent of speed = %.2f ohms'%R2

(a)Value of external resistance when the load torque is independent of speed = 0.98 ohms
(b)Value of external resistance when the load torque is proportional to speed = 1.08 ohms
(a)Value of external resistance when the load torque is independent of speed = 1.20 ohms


## Exa:2.43 Pg No: 204¶

In [5]:
from math import sqrt
V=240 #  volts
P=10000 #  watts
R_a=0.25 #  ohms
R_f=160 #  ohms
I_f=V/R_f
I_L=5.2 #  amperes
I_ao=I_L-I_f
W=V*I_ao-I_ao**2*R_a
I_a=(V-sqrt(V**2-4*R_a*(P+W)))/(2*R_a)
P_in=P+W+I_a**2*R_a+I_f**2*R_f
Eff=P/P_in
print 'Efficiency of the motor = %.2f %%'%(Eff*100)

Efficiency of the motor = 85.13 %


## Exa:2.44 Pg No: 205¶

In [1]:
V=440 #  volts
N_1=1000 #  rpm
N_2=1050 #  rpm
r=N_1/N_2
V_drop=2*(V-V*r)
print 'Armature voltage drop = %.2f volts'%V_drop

Armature voltage drop = 880.00 volts


## Exa:2.45 Pg No: 205¶

In [2]:
V=220 #  volts
R_a=2.5 #  ohms
N_1=859 #  rpm
I_ao=0
I_a=8 #  amperes
E_b1=V-I_a*R_a
E_bo=V-I_ao*R_a
N_o=N_1*E_bo/E_b1
print 'No Load Speed = %.2f RPM'%N_o

No Load Speed = 944.90 RPM


## Exa:2.46 Pg No: 206¶

In [4]:
from math import sqrt
V=220 #  volts
R_a=0.2 #  ohms
R_f=110 #  ohms
N_1=700 #  rpm
N_2=900 #  rpm
T_a1=90 #  N-m
T_a2=70 #  N-m
I_1=27 #  amperes
I_f=V/R_f
I_a1=I_1-I_f
E_b1=V-I_a1*R_a
x=(V+sqrt(V**2-4*276.43*4.168))/(2*276.43)
print 'percentage reduction in feild flux = %.2f %%'%((1-x)*100)
I_f2=x*I_f
R=(V-I_f2*R_f)/I_f2
print 'Value of additional resistance = %.2f ohms'%R

percentage reduction in feild flux = 22.36 %
Value of additional resistance = 31.67 ohms


## Exa:2.47 Pg No: 207¶

In [1]:
from math import sqrt
V=400 #  volts
R_f=200 #  ohms
I_1=25 #  amperes
I_f=V/R_f
I_a1=I_1-I_f
x=(-V+sqrt(V**2+4*345*400))/(2*345)
print 'New Speed is= %.2f'%(x*100)
print 'percent of original speed'

New Speed is= 64.32
percent of original speed