Chapter 9 - D C Motors

Example 1 - pg 9_14

In [3]:
#Chapter-9,Example9_1,pg 9_14
#calculate the emf for lap and wave wounds
#given
P=4.
Z=440.
phi=0.07#flux(in Wb)
N=900.
#for lap-wound
#calculations
A=P
E=phi*P*N*Z/(60*A)
#results
print"e.m.f for lap wound (V) = ",E
#for wave wound
A=2.
E=phi*P*N*Z/(60*A)
print"e.m.f for wave wound (V) = ",E
e.m.f for lap wound (V) =  462.0
e.m.f for wave wound (V) =  924.0

Example 2 - pg 9_15

In [4]:
#Chapter-9,Example9_2,pg 9_15
#calculate the speed and emf
#given
P=4.
phi=21.*10**-3#flux(in Wb)
N=1120.
C=42.#coils
tpC=8.#turns per coil
#calculations and results
t=C*tpC#total turns
Z=2*t
#for lap wound
A=P
E=phi*P*N*Z/(60*A)
print"e.m.f for lap wound (V) = ",E
#for wave wound
A=2.
E=263.424
N=E*60*A/(phi*P*Z)
print"speed of generator for wave wound (rpm) = ",N
e.m.f for lap wound (V) =  263.424
speed of generator for wave wound (rpm) =  560.0

Example 3 - pg 9_20

In [5]:
#Chapter-9,Example9_3,pg 9_20
#calculate the back emf 
#given
V=220.
Ia=30.
Ra=0.75
#calculations
Eb=V-Ia*Ra
#results
print"back e.m.f of motor (V) = ",Eb
back e.m.f of motor (V) =  197.5

Example 4 - pg 9_21

In [6]:
#Chapter-9,Example9_4,pg 9_21
#calculate the back emf and speed of motor
P=4.
A=P
V=230.
Ra=0.6
Z=250.
phi=30.*10**-3#flux(in Wb)
Ia=40.
#calculations
Eb=V-Ia*Ra
N=Eb*60*A/(phi*P*Z)
#results
print"back e.m.f (V) = ",Eb
print"speed of motor (rpm) = ",N
back e.m.f (V) =  206.0
speed of motor (rpm) =  1648.0

Example 5 - pg 9_24

In [7]:
#Chapter-9,Example9_5,pg 9_24
#calculate the gross torque
#given
P=4.
A=P
Z=480.
phi=20.*10**-3#flux(in Wb)
Ia=50.
#calculations
Ta=0.159*phi*Ia*(P*Z/A)
#results
print"gross torque (N-m) = ",Ta
gross torque (N-m) =  76.32

Example 6 - pg 9_25

In [8]:
#Chapter-9,Example9_6,pg 9_25
#calculate the induced emf, armature current, stray losses and loss torque
import math
#given
P=4.
A=P
No=1000.#speed of motor
Z=540.
V=230.
phi=25.*10**-3#flux(In Wb)
Ra=0.8
#calculations
Ebo=phi*P*No*Z/(60*A)#induced e.m.f
Iao=(V-Ebo)/Ra#armature current
SL=Ebo*Iao#stray losses
wo=2*math.pi*No/60#angular velocity
Tf=Ebo*Iao/wo#loss torque
#results
print"induced e.m.f (V) = ",Ebo
print"armature current (A) = ",Iao
print"stray losses (W) = ",SL
print"loss torque (Nm) = ",round(Tf,3)
induced e.m.f (V) =  225.0
armature current (A) =  6.25
stray losses (W) =  1406.25
loss torque (Nm) =  13.429

Example 7 - pg 9_37

In [9]:
#Chapter-9,Example9_7,pg 9_37
#calculate the speed of motor
#given
P=4.
Z=200.
V=250.
A=2.
phi=25.*10**-3
Ia=60.
#calculations
Il=Ia
Ra=0.15
Rse=0.2
Eb=V-Ia*(Ra+Rse)
N=Eb*60*A/(phi*P*Z)
#results
print"speed of motor (rpm) = ",N
speed of motor (rpm) =  1374.0

Example 8 - pg 9_38

In [10]:
#Chapter-9,Example9_8,pg 9_38
#calculate the back emf
#given
V=250.
Il=20.
Ra=0.3
Rsh=200.
#calculations
Ish=V/Rsh
Ia=Il-Ish
Eb=V-Ia*Ra
#results
print"back e.m.f (V) = ",Eb
back e.m.f (V) =  244.375

Example 9 - pg 9_38

In [11]:
#Chapter-9,Example9_9,pg 9_38
#calculate the speed at full load
#given
No=1000.
V=220.
Rsh=110.
Ra=0.3
#calculations
Ish=V/Rsh
Ilo=6.
Iao=Ilo-Ish
Rao=0.3
Ebo=V-Iao*Ra
#on full load
Il=50
IaFL=Il-Ish
EbFL=V-IaFL*Ra
#N=k*Eb/phi
NFL=No*EbFL/Ebo
#results
print"speed at full load (rpm) = ",round(NFL,2)
speed at full load (rpm) =  939.67

Example 10 - pg 9_39

In [12]:
#Chapter-9,Example9_10,pg 9_39
#calculate the speed of motor on new load
#given
N1=800.
I1=20.
V=250.
Ia1=I1
I2=50.
Ia2=I2
Ra=0.2
Ise1=I1
Ise2=I2
Rse=0.3
#calculations
Eb1=V-Ia1*Ra-Ise1*Rse
Eb2=V-Ia2*Ra-Ise2*Rse
#from speed equation
N2=N1*(Eb2/Eb1)*(Ia1/Ia2)
#results
print"speed of motor on new load (rpm) = ",N2
speed of motor on new load (rpm) =  300.0

Example 11 - pg 9_45

In [13]:
#Chapter-9,Example9_11,pg 9_45
#calculate the new current and speed
#given
V=250.
Rsh=250.
Ra=0.25
Rx=Rsh
Ia1=20.
#calculations
Ish1=V/Rsh
Ish2=V/(Rsh+Rx)
N1=1500.
Eb1=V-Ia1*Ra
#phi=k*Ish
#T1=T2
Ia2=Ish1*Ia1/Ish2#new current
Eb2=V-Ia2*Ra
#from speed equation
N2=N1*(((Eb1/Eb2)*(Ish2/Ish1))**-1)#new speed
#results
print"new current (A) = ",Ia2
print"new speed (rpm) = ",round(N2,3)
new current (A) =  40.0
new speed (rpm) =  2938.776

Example 12 - pg 9_46

In [14]:
#Chapter-9,Example9_12,pg 9_46
#calculate the resistance in shunt field
#given
import math
V=250.
Ra=0.5
Rsh=250.
Ia1=20.
Ish1=V/Rsh
Eb1=V-Ia1*Ra
N1=600.
N2=800.
#T1=T2
#Ish1*Ia1=Ish2*Ia2
#Ish2*Ia2=20............(1)
#(N1/N2)=(Eb1/Eb2)*(Ish2/Ish1)...........(2)
#using (1) and (2)
#240*(Ish2^2)-187.5*Ish2+7.5=0.........(3)
b=-187.5
a=240
c=7.5
#calculations
Ish2=(-b+math.sqrt(((b**2)-4*a*c)))/(2*a)#neglecting lower value
Rx=(V/Ish2)-Rsh
#results
print"resistance in shunt field (ohm) = ",round(Rx,3)
resistance in shunt field (ohm) =  88.313

Example 13 - pg 9_51

In [15]:
#Chapter-9,Example9_13,pg 9_51
#calculate the speed of motor
#given
import math
V=250.
Ra=0.15
Rx=0.1
Rse=0.1
N1=800.
Ise1=30.
Ia1=30.#Ia1=Ise1
I1=Ia1
#phi=k*Ise
#T2=T1+0.5*T1(increased by 50%)..........(1)
#Ise2=Ia2*Rx/(Rx+Rse)
#putting values of Rx and Rse Ise2=0.5*Ia2.........(2)
#putting (1) and (2) in torque equation
#calculations
Ia2=math.sqrt(2700)
Ise2=0.5*Ia2#from (2)
Eb1=V-Ia1*Ra-Ise1*Rse
Eb2=V-Ia2*Ra-Ise2*Rse
#using speed equation
N2=N1*Eb2*Ise1/(Eb1*Ise2)
#results
print"speed of motor (rpm) = ",round(N2,3)
speed of motor (rpm) =  912.743

Example 14 - pg 9_52

In [16]:
#Chapter-9,Example9_14,pg 9_52
#calculate the speed of motor
#given
V=220.
Ise1=15.
Ia1=Ise1
Ia2=10.
Ise2=Ia2
I2=Ia2
N1=900.
Ra=0.5
Rse=0.5
Rx=4.
#calculations
Eb1=V-Ia1*Ra-Ise1*Rse
Eb2=V-Ia2*Ra-Ise2*Rse-I2*Rx
N2=N1*Eb2*Ise1/(Eb1*Ise2)
#results
print"speed of motor (rpm) = ",round(N2,4)
speed of motor (rpm) =  1119.5122

Example 15 - pg 9_64

In [18]:
#Chapter-9,Example9_15,pg 9_64
#calculate the useful torque and efficiency at load
#given
import math
P=6.
V=500.
A=2.#wave wound
Z=1200.
phi=20*10**-3#flux
Ra=0.5
Rsh=250.
Il=20.
#calculations
Ish=V/Rsh
Ia=Il-Ish
Eb=V-Ia*Ra
N=Eb*60*A/(phi*P*Z)
Pm=Eb*Ia#mechanical power
w=2*math.pi*N/60#angular velocity
Tg=Pm/w
ML=900#mechanical losses
Pout=Pm-ML
Tsh=Pout/w#usefull torque
Pin=V*Il
n=Pout*100/Pin#efficiency at load
#results
print"useful torque (Nm) = ",round(Tsh,2)
print"efficiency at load (percent) = ",n
useful torque (Nm) =  185.26
efficiency at load (percent) =  79.38

Example 16 - pg 9_65

In [19]:
#Chapter-9,Example9_16,pg 9_65
#calculate the speed of motor
#given
V=120.
Ra=0.2
Rsh=60.
#for full load
Il1=40.
N1=1800.
#for shunt motor
#calculations
Ish=V/Rsh
Ia1=Il1-Ish
Eb1=V-Ia1*Ra
#for half load T2=T1/2
Ia2=Ia1*0.5#T=k*Ia
Eb2=V-Ia2*Ra
N2=N1*Eb2/Eb1#from torque equation
#results
print"speed of motor (rpm) = ",round(N2,2)
speed of motor (rpm) =  1860.85

Example 17 - pg 9_66

In [21]:
#Chapter-9,Example9_17,pg 9_66
#calculate the speed of generator
#given
Ra=0.08
Eb1=242.
V=250.
Ia=87.
Vt=V#generator supply
Nm=1500.
#calculations
Ia1=(V-Eb1)/Ra
#at start N=0, Eb=0
Ias=V/Ra#Ia(start)
Ia2=120
Eb2=V-Ia2*Ra
Eg=Vt+Ia*Ra#generator e.m.f
Ng=Nm*Eg/Eb1#speed as generator
#results
print"speed as generator (rpm) = ",round(Ng,1)
speed as generator (rpm) =  1592.7

Example 18 - pg 9_67

In [22]:
#Chapter-9,Example9_18,pg 9_67
#calculate the gross mechanical power,stray losses and no load speed
#given
import math
V=250.
Po=59680.
Rsh=250.
Ra=0.04
n=80.#efficiency
N1=1200.
#calculations and results
Il=Po*100/(V*n)#Pi=V*Il
Ish=V/Rsh
Ia=Il-Ish
Eb=V-Ia*Ra
Pm=Eb*Ia#gross mechanical power
SL=Pm-Po#stray losses
print"gross mechanical power (kW) = ",round(Pm/1000.,3)
print"stray losses (W) = ",round(SL,2)
#on no load
#Pg=S, Ebo*Iao=SL..........(1)
#Ebo=V-Iao*Ra............(2)
#putting (2) in (1)
#(Iao^2)-6250*Iao+278303.24=0
b=-6250.
a=1.
c=278303.24
Iao=(-b-math.sqrt((b**2)-4*a*c))/(2*a)
I=Iao-Ish#current drawn on no load
Ebo=V-Iao*Ra
No=N1*Ebo/Eb
print"no load speed (rpm) = ",round(No,4)
gross mechanical power (kW) =  70.812
stray losses (W) =  11132.13
no load speed (rpm) =  1250.9121

Example 19 - pg 9_69

In [23]:
#Chapter-9,Example9_19,pg 9_69
#calculate the full load speed
#given
V=250.
P=4.
Ra=0.1
Rsh=125.
Vbr=2.#brush drop
#no load condition
Ilo=4.
No=1200.
Il1=61.
#calculations
Ish=V/Rsh
Iao=Ilo-Ish
Ebo=V-Iao*Ra-Vbr
#full load condition
#phi1=phio-o.o5*phio       (weakened by 5%)
#phi=phi1/phio
phi=0.95
Ia1=Il1-Ish
Eb1=V-Ia1*Ra-Vbr
N1=No*Eb1/(Ebo*phi)
#results
print"full load speed (rpm) = ",round(N1,3)
full load speed (rpm) =  1234.102

Example 20 - pg 9_70

In [24]:
#Chapter-9,Example9_20,pg 9_70
#calculate the full load speed, speed regulation, hp rating and efficiency
#given
V=250.
Ra=0.15
Rsh=166.67
No=1280.
Il1=67.
#calculations
Ish=V/Rsh
Ia1=Il1-Ish
Eb1=V-Ia1*Ra
#on no load
Ilo=6.5
Ish=1.5
Iao=Ilo-Ish
Ebo=V-Iao*Ra
N1=Eb1*No/Ebo
Sr=(No-N1)*100/No#speed regulation
SL=Ebo*Iao
Po=Eb1*Ia1-SL#full load shaft output
hp=Po/746.#horse power rating
Pi=V*Il1
n=Po*100./Pi
#results
print"full load speed (rpm) = ",round(N1,3)
print"speed regulation (percent) = ",round(Sr,2)
print"hp rating of machine (hp) = ",round(hp,2)
print"full load efficiency (percent) = ",round(n,2)
print "The answer differs from the textbook due to rounding off error"
full load speed (rpm) =  1233.396
speed regulation (percent) =  3.64
hp rating of machine (hp) =  19.42
full load efficiency (percent) =  86.48
The answer differs from the textbook due to rounding off error

Example 21 - pg 9_71

In [25]:
#Chapter-9,Example9_21,pg 9_71
#calculate the speed of motor
import math
#given
Ra=0.1
V=110.
P=4.
Ia1=50.
I1=Ia1
Rse=0.02
N1=700
#calculations
Eb1=V-Ia1*Ra-Ia1*Rse
#using torque  equation T=k*phi*Ia
Ia2=math.sqrt(2)*Ia1
Eb2=V-Ia2*Ra-Ia2*Rse/4#parallel speed groups
#using speed equation N=k*Eb/phi
N2=N1*Eb2*2*Ia1/(Eb1*Ia2)
#results
print"speed of motor (rpm) = ",round(N2,3)
speed of motor (rpm) =  976.389

Example 22 - pg 9_73

In [26]:
#Chapter-9,Example9_22,pg 9_73
#calculate the new speed of motor
#given
P=4.
Ia1=50.
N1=2000.
V=230.
#calculations
#coils connected in series
#phi1=k*Ia1*(4*n)=k*200*n
#coils connected in parallel groups of series coils
#phi2=k*((Ia2*2*n/2)+(Ia2*2*n/2))=k*2*n*Ia2
#phi1/phi2=100/Ia2........(1)
#N1/N2=phi2/phi1........(2)
#T=kN**2..........(3)
Ia2=(Ia1*(100**3))**(1./4)#using (1) in (3)
N2=(((N1**3)*Ia2)/Ia1)**(1./3)
#results
print"new speed of motor (rpm) = ",round(N2,3)
new speed of motor (rpm) =  2378.414

Example 24 - pg 9_76

In [27]:
#Chapter-9,Example9_24,pg 9_76
#calculate the extra resistance to reduce speed
import math
#given
V=200.
Ia1=30.
Ra=0.75
Rse=0.75
#calculations
R=Ra+Rse
Eb1=V-Ia1*R
#N2=0.6*N1
N=0.6#N=N2/N1
#using T=k*Ia**2 and T=k*N**3
Ia2=math.sqrt(((0.6**3)*30**2))
#using speed equation N=k*Eb/Ia
Eb2=N*Eb1*Ia2/Ia1
#Eb2=V-Ia2*(R+Rx)
Rx=-(Eb2-V+Ia2*R)/Ia2
#results
print"extra resistance to reduce speed (ohm) = ",round(Rx,3)
extra resistance to reduce speed (ohm) =  9.744

Example 25 - pg 9_77

In [28]:
#Chapter-9,Example9_25,pg 9_77
#calculate the new supply voltage
#given
R=1.
V1=230.
N1=300.
Ia1=15.
N2=375.
#calculations
#using torque equation T=k*N^2
Ia2=N2*Ia1/N1
#using speed equation N=k*Eb/Ia........(1)
Eb1=V1-Ia1*R
#case-2
#Eb2=V2-Ia2*R=V2-18.75......(2)
#putting (2) in (1)
V2=(N2*Eb1*Ia2/(N1*Ia1))+18.75
#results
print"new supply voltage (V) = ",V2
new supply voltage (V) =  354.6875

Example 26 - pg 9_78

In [29]:
#Chapter-9,Example9_26,pg 9_78
#calculate the power input and efficiency of motor
#given
import math
V=400.
Po1=18.5*10**3
Pi1=22.5*10**3
Rsh=200.
Ra=0.4
Po2=9.*10**3
#calculations
I1=Pi1/V
Ish=V/Rsh
Ia1=I1-Ish
Acl=(Ia1**2)*Ra#armature copper loss
Scl=(Ish**2)*Rsh#shunt feild copper loss
TL=Pi1-Po1#total losses
SFl=TL-(Acl+Scl)#stray and friction loss
#case-2
Pm=Po2+SFl#mechanical power
#Pm=Eb2*Ia2.........(1)
#Eb2=V-Ia2*Ra.......(2)
#using (1) and (2)
#0.4*(Ia2**2)-400*Ia2+11022.75=0
a=0.4
b=-400
c=11022.775
Ia2=(-b-math.sqrt((b**2)-4*a*c))/(2*a)#neglecting higher value
Pi2=Po2+(Ia2**2)*Ra+(Ish**2)*Rsh+SFl
n=Po2*100/Pi2#efficiency
#results
print"power input in case-2 (kW) = ",round(Pi2/1000.,3)
print"efficiency of motor = ",round(n,3)
power input in case-2 (kW) =  12.145
efficiency of motor =  74.107

Example 27 - pg 9_79

In [30]:
#Chapter-9,Example9_27,pg 9_79
#calculate the maximum efficiency
#given
import math
V=250.
Ilo=4.
Ra=1.
Rsh=250.
Il1=20.
#calculations
Ish=V/Rsh
Iao=Ilo-Ish
Ia1=Il1-Ish
Ebo=V-Iao*Ra
Po=Ebo*Iao
Eb1=V-Ia1*Ra
P1=Eb1*Ia1
Pout=P1-Po
Pi=V*Il1
n=Pout*100/Pi
#fro max. efficiency
#const. losses=variable losses
Ia=math.sqrt(Po+(Ish**2)*Rsh)
Ebm=V-Ia*Ra
Pm=Ebm*Ia
Pout=Pm-Po
Pi=V*(Ia+Ish)
nm=Pout*100/Pi
#results
print"maximum efficiency = ",round(nm,2)
maximum efficiency =  75.59

Example 28 - pg 9_81

In [31]:
#Chapter-9,Example9_28,pg 9_81
#calculate the back emf
#given
V=250.
FLo=16.*10**3#full scale output
n=80.
#calculations
I=FLo*100/n#input
Il=I/V
Il=Il
Ia=1.5*Il
#at start
Ra=V/Ia
Rac=0.18#Ra actual
Ras=Ra-Rac#Ra starter
Ia=Il#Ia drops as motor starts
Eb=V-Ia*(Ra)
#results
print"back e.m.f (V) = ",round(Eb,2)
back e.m.f (V) =  83.33

Example 29 - pg 9_82

In [33]:
#Chapter-9,Example9_29,pg 9_82
#calculate the electromagnetic torque, flux and efficiency
#given
import math
Po=20.*735.5#(in W)
V=230.
N=1150.
P=4.
A=P
Z=882.
Ia=73.
Ish=1.6
#calculations
T=60*Po/(2*math.pi*N)
phi=T*A/(0.159*Ia*P*Z)#flux per pole
Il=Ia+Ish
Pin=V*Il
n=Po*100/Pin
#results
print"electromagnetic torque (Nm) = ",round(T,4)
print"flux per pole (mWb) = ",round(phi*1000.,4)
print"efficiency of motor (percent) = ",round(n,3)
electromagnetic torque (Nm) =  122.148
flux per pole (mWb) =  11.9316
efficiency of motor (percent) =  85.733

Example 30 - pg 9_83

In [34]:
#Chapter-9,Example9_30,pg 9_83
#calculate the speed of motor
#given
Pr=12.*10**3#rated output
V=200.
Rsh=80.
N1=800.
n=0.9#efficiency
#calculations
Out=0.8*Pr#output is 80% of rated
In=Out/n#input
TL=In-Out
#for max. efficiency
Iln=70#new current
#TL=Wc+(Ia1^2)*Ra
#bur Wc=(Ia1^2)*Ra
Wc=TL/2
Il=In/V
Ish=V/Rsh
Ia1=Il-Ish
Ra=Wc/(Ia1**2)
Ia2=Iln-Ish
Wcn=Wc#const. losses remain same
TL=(Ia2**2)*Ra+Wcn
Pi=V*Iln
n=(Pi-TL)*100/Pi
Eb1=V-Ia1*Ra
Eb2=V-Ia2*Ra
N2=N1*Eb2/Eb1
#results
print"speed of motor (rpm) = ",round(N2,3)
speed of motor (rpm) =  785.478

Example 31 - pg 9_85

In [35]:
#Chapter-9,Example9_31,pg 9_85
#calculate the efficiency of motor
#given
Po=8.952*10**3
V=440.
Ra=1.1
Rsh=650
Rint=0.4
Rreg=50.
Ml=450.
Vbr=2.#brush drop
Il=24.
#calculations
Rat=Ra+Rint#series connection
Rsht=Rsh+Rreg#series connection
Ish=V/Rsht
Ia=Il-Ish
Acl=(Ia**2)*Rat#armature copper loss
Fcl=(Ish**2)*Rsht#feild copper loss
Bdl=Vbr*Ia#brush drop loss
TL=Acl+Fcl+Bdl+Ml
n=Po*100/(Po+TL)
#results
print"efficiency of motor (percent) = ",round(n,3)
efficiency of motor (percent) =  84.896

Example 32 - pg 9_85

In [36]:
#Chapter-9,Example9_32,pg 9_85
#calculate the speed of motors
#given
#for first motor
N1=700.
R=0.5#Ra+Rse
I1=70.
V=500.
#calculations
Eb1=V-I1*R
K1=Eb1/(N1*I1)
#for second motor
N2=750.
R=0.5
I2=70.
V=500.
Eb2=V-I2*R
K2=Eb2/(N2*I2)
#motors in series
It=70.
Rt=2*R
Eb=V-It*Rt
N=Eb/(K1*It+K2*It)
#results
print"speed of motors (rpm) = ",round(N,3)
speed of motors (rpm) =  334.816

Example 33 - pg 9_86

In [37]:
#Chapter-9,Example9_33,pg 9_86
#calculate the maximum efficiency output
#given
import math
Po=7.46*10**3
V=250
Ilo=5.
Ra=0.5
Rsh=250.
#calculations
Ish=V/Rsh
Iao=Ilo-Ish
Acl=(Iao**2)*Ra
Fcl=(Ish**2)*Rsh
Pi=V*Ilo
FWl=Pi-Acl-Fcl#friction and windage loss
#Pin=Eb*Ia=(V-Ia*Ra)*Ia
#0.5*(Ia**2)-250*Ia+8452=0
b=-250
a=0.5
c=8452
Ia=(-b-math.sqrt((b**2)-4*a*c))/(2*a)#neglecting higher value
TL=(Ia**2)*Ra+(Ish**2)*Rsh+FWl
n=Po*100/(Po+TL)
#for max. efficiency
Ia=math.sqrt((FWl+Fcl)/Ra)
Eb=V-Ia*Ra
Pm=Eb*Ia
#Po at nmax
Po=Pm-FWl
#results
print"maximum efficiency output (W) = ",round(Po,3)
maximum efficiency output (W) =  10225.936

Example 34 - pg 9_87

In [38]:
#Chapter-9,Example9_33,pg 9_87
#calculate the speed of motor in both cases
#given
V=500.
Ra=1.2
Rsh=500.
#calculations
Ish=V/Rsh
Ilo=4.
Iao=Ilo-Ish
Ebo=V-Iao*Ra
Il1=26.
Ish1=1.
Ia1=Il1-Ish1
Eb1=V-Ia1*Ra
No=1000.
N1=No*Eb1/Ebo
print"speed of motor case-1 (rpm) = ",round(N1,3)
Rx=2.3#connected in series with armature
Eb2=V-Ia1*(Ra+Rx)
N2=N1*Eb2/Eb1
#results
print"speed of motor case-2 (rpm) = ",round(N2,3)
Ish3=Ish1-0.15*Ish1#reduced by 15%
Ia3=Ish1*Ia1/(Ish3)
Eb3=V-Ia3*Ra
N3=N1*Eb3*Ish1/(Eb1*Ish3)
print"speed of motor case-3 (rpm) = ",round(N3,4)
speed of motor case-1 (rpm) =  946.817
speed of motor case-2 (rpm) =  830.983
speed of motor case-3 (rpm) =  1101.3554