In [1]:

```
from __future__ import division
import math
#initializing the variables:
Z = 600;# no. of conductors
c = 2;# for a wave winding
p = 4;# no. of pairs
n = 625/60;# in rev/sec
Phi = 20E-3;# in Wb
#calculation:
#Generated e.m.f., E = 2*p*Phi*n*Z/c
E = 2*p*Phi*n*Z/c
#Results
print "\n\n Result \n\n"
print "\n the generated e.m.f is ",round(E,2)," V "
```

In [2]:

```
from __future__ import division
import math
#initializing the variables:
Z = 50*16;# no. of conductors
p = 1;# let no. of pairs
c = 2*p;# for a lap winding
Phi = 30E-3;# in Wb
E = 240;# in Volts
#calculation:
#Generated e.m.f., E = 2*p*Phi*n*Z/c
#Rearranging gives, speed
n = E*c/(2*p*Phi*Z)
#Results
print "\n\n Result \n\n"
print "\n the speed at which the machine must be driven is ",round(n,2)," rev/sec "
```

In [3]:

```
from __future__ import division
import math
#initializing the variables:
Z = 1200;# no. of conductors
p = 1;# let, no. of pairs
c = 2*p;# for a lap winding
Phi = 30E-3;# in Wb
n = 500/60;# in rev/sec
#calculation:
#Generated e.m.f., E = 2*p*Phi*n*Z/c
E = 2*p*Phi*n*Z/c
#Results
print "\n\n Result \n\n"
print "\n Generated e.m.f. is ",round(E,2)," V "
```

In [4]:

```
from __future__ import division
import math
#initializing the variables:
Z = 1200;# no. of conductors
p = 4;# let, no. of pairs
c = 2;# for a wave winding
Phi = 30E-3;# in Wb
n = 500/60;# in rev/sec
#calculation:
#Generated e.m.f., E = 2*p*Phi*n*Z/c
E = 2*p*Phi*n*Z/c
#Results
print "\n\n Result \n\n"
print "\n Generated e.m.f. is ",round(E,2)," V "
```

In [1]:

```
from __future__ import division
import math
#initializing the variables:
E1 = 150; # in Volts
x = 0.2;
#calculation:
E2 = E1*(1- x)
#Results
print "\n\n Result \n\n"
print "\n Generated e.m.f. is ",round(E2,2)," V "
```

In [5]:

```
from __future__ import division
import math
#initializing the variables:
n1 = 30;# in rev/sec
E1 = 200;# in Volts
n2 = 20;# in rev/sec
E2 = 250;# in Volts
#calculation:
#generated e.m.f., E proportional to phi*w and since w = 2*pi*n, then
# E proportional to phi*n
# E1/E2 = Phi1*n1/(Phi2*n2)
# let Phi2/Phi1 = Phi
Phi = E2*n1/(E1*n2)
Phi_inc = (Phi - 1)*100#/in percent
#Results
print "\n\n Result \n\n"
print "\n percentage increase in the flux per pole is ",round(Phi_inc,2)," percent "
```

In [6]:

```
from __future__ import division
import math
#initializing the variables:
Ra = 0.30;# in ohms
Ia = 30;# in Amperes
E = 200;# in Volts
#calculation:
#terminal voltage,
#V = E - Ia*Ra
V = E - Ia*Ra
#Results
print "\n\n Result \n\n"
print "\n terminal voltage of a generator is ",round(V,2)," V "
```

In [7]:

```
from __future__ import division
import math
#initializing the variables:
RL = 60;# in ohms
Ia = 8;# in Amperes
Ra = 1;# in ohms
#calculation:
#terminal voltage,
#V = Ia*RL
V = Ia*RL
#Generated e.m.f., E
E = V + Ia*Ra
#Results
print "\n\n Result \n\n"
print "\n (a)terminal voltage is ",round(V,2)," V "
print "\n (b)generated e.m.f. is ",round(E,2)," V "
```

In [8]:

```
from __future__ import division
import math
#initializing the variables:
E1 = 150;# in Volts
n1 = 20;# in rev/sec
Phi1 = 0.10;# in Wb
n2 = 25;# in rev/sec
Phi2 = 0.10;# in Wb
n3 = 20;# in rev/sec
Phi3 = 0.08;# in Wb
n4 = 24;# in rev/sec
Phi4 = 0.07;# in Wb
#calculation:
#generated e.m.f., E proportional to phi*w and since w = 2*pi*n, then
# E proportional to phi*n
# E1/E2 = Phi1*n1/(Phi2*n2)
E2 = E1*Phi2*n2/(Phi1*n1)
E3 = E1*Phi3*n3/(Phi1*n1)
E4 = E1*Phi4*n4/(Phi1*n1)
#Results
print "\n\n Result \n\n"
print "\n (a)the generated e.m.f is ",round(E2,2)," V "
print "\n (b)generated e.m.f. is ",round(E3,2)," V "
print "\n (c)generated e.m.f. is ",round(E4,2)," V "
```

In [9]:

```
from __future__ import division
import math
#initializing the variables:
Ps = 20000;# in Watts
Vs = 200;# in Volts
Rs = 0.1;# in ohms
Rf = 50;# in ohms
Ra = 0.04;# in ohms
#calculation:
#Load current, I
Is = Ps/Vs
#Volt drop in the cables to the load
Vd = Is*Rs
#Hence terminal voltage,
V = Vs + Vd
#Field current, If
If = V/Rf
#Armature current
Ia = If + Is
#Generated e.m.f. E
E = V + Ia*Ra
#Results
print "\n\n Result \n\n"
print "\n (a)terminal voltage is ",round(V,2)," V "
print "\n (b)generated e.m.f. is ",round(E,2)," V "
```

In [12]:

```
from __future__ import division
import math
#initializing the variables:
Is = 80;# in amperes
Vs = 200;# in Volts
Rf = 40;# in ohms
Rse = 0.02;# in ohms
Ra = 0.04;# in ohms
#calculation:
#Volt drop in series winding
Vse = Is*Rse
#P.d. across the field winding = p.d. across armature
V1 = Vs + Vse
#Field current, If
If = V1/Rf
#Armature current
Ia = If + Is
#Generated e.m.f. E
E = V1 + Ia*Ra
#Results
print "\n\n Result \n\n"
print "\n generated e.m.f. is ",round(E,2)," V "
```

In [13]:

```
from __future__ import division
import math
#initializing the variables:
Ps = 10000;# in Watt
Pl = 600;# in Watt
Ra = 0.75;# in ohms
Rf = 125;# in ohms
V = 250;# in Volts
#calculation:
#Output power Ps = V*I
#from which, load current I
I = Ps/V
#Field current, If
If = V/Rf
#Armature current
Ia = If + I
#Efficiency,
eff = Ps*100/((V*I) + (Ia*Ia*Ra) + (If*V) + (Pl))# in Percent
#Results
print "\n\n Result \n\n"
print "\n Efficiency is ",round(eff,2)," percent "
```

In [14]:

```
from __future__ import division
import math
#initializing the variables:
Ra = 0.2;# in ohms
V = 240;# in Volts
Ia = 50;# in Amperes
#calculation:
#For a motor, V = E + Ia*Ra
E = V - Ia*Ra
#Results
print "\n\n Result \n\n"
print "\n back e.m.f. is ",round(E,2)," V "
```

In [15]:

```
from __future__ import division
import math
#initializing the variables:
Ra = 0.25;# in ohms
V = 300;# in Volts
Ig = 100;# in Amperes
Im = 80;# in Amperes
#calculation:
#As a generator, generated e.m.f.,
# E = V + Ia*Ra
Eg = V + Ig*Ra
#For a motor, generated e.m.f. (or back e.m.f.),
# E = V - Ia*Ra
E = V - Im*Ra
#Results
print "\n\n Result \n\n"
print "\n (a)As a generator, generated e.m.f. is ",round(Eg,2)," V "
print "\n (b)back e.m.f. is ",round(E,2)," V "
```

In [16]:

```
from __future__ import division
import math
#initializing the variables:
p = 4;
c = 2;# for a wave winding
Phi = 25E-3;# Wb
Z = 900;
Ia = 30;# in Amperes
#calculation:
#torque T = p*Phi*Z*Ia/(pi*c)
T = p*Phi*Z*Ia/(1*math.pi*c)
#Results
print "\n\n Result \n\n"
print "\n the torque exerted is ",round(T,2)," Nm "
```

In [17]:

```
from __future__ import division
import math
#initializing the variables:
V = 350;# in Volts
Ra = 0.5;# in ohms
n = 15;# in rev/sec
Ia = 60;# in Amperes
#calculation:
#Back e.m.f. E = V - Ia*Ra
E = V - Ia*Ra
#torque T = E*Ia/(2*n*pi)
T = E*Ia/(2*n*math.pi)
#Results
print "\n\n Result \n\n"
print "\n the torque exerted is ",round(T,2)," Nm "
```

In [18]:

```
from __future__ import division
import math
#initializing the variables:
p = 1;# let
c = 2*p;# for a lap winding
Phi = 20E-3;# Wb
Z = 500;
V = 250;# in Volts
Ra = 1;# in ohms
Ia = 40;# in Amperes
#calculation:
#Back e.m.f. E = V - Ia*Ra
E = V - Ia*Ra
#E.m.f. E = 2*p*Phi*n*Z/c
# rearrange,
n = E*c/(2*p*Phi*Z)
#torque T = E*Ia/(2*n*pi)
T = E*Ia/(2*n*math.pi)
#Results
print "\n\n Result \n\n"
print "\n (a)speed n is ",round(n,2)," rev/sec "
print "\n (b)the torque exerted is ",round(T,2)," Nm "
```

In [19]:

```
from __future__ import division
import math
#initializing the variables:
T1 = 25;# in Nm
T2 = 35;# in Nm
Ia1 = 16;# in Amperes
V = 100;# in Volts
x = 0.15;
#calculation:
#the shaft torque T of a generator is proportional to (phi*Ia),
#where Phi is the flux and Ia is the armature current. Thus, T = k*Phi*Ia, where k is a constant.
#The torque at flux phi1 and armature current Ia1 is T1 = k*Phi1*Ia1.
#similarly T2 = k*Phi2*Ia2
Ia2 = T2*Ia1/(0.85*T1)
#Results
print "\n\n Result \n\n"
print "\n armature current at the new value of torque is ",round(Ia2,2)," A "
```

In [20]:

```
from __future__ import division
import math
#initializing the variables:
T = 12;# in Nm
I = 15;# in Amperes
V = 100;# in Volts
n = 1500/60;# in rev/sec
#calculation:
#the efficiency of a generator = (output power/input power)*100 %
#The output power is the electrical output, i.e. VI watts.
#The input power to a generator is the mechanical power in the shaft driving the generator,
#i.e. T*w or T(2*pi*n) watts, where T is the torque in Nm and n is speed of rotation in rev/s. Hence, for a generator
#efficiency = V*I*100/(T*2*pi*n) %
eff = V*I*100/(T*2*math.pi*n)# in Percent
#The input power = output power + losses
# hence, T*2*math.pi*n = V*I + losses
Pl = T*2*math.pi*n - V*I
#Results
print "\n\n Result \n\n"
print "\n (a) efficiency is ",round(eff,2)," % "
print "\n (b) power loss is ",round(Pl,2)," W "
```

In [21]:

```
from __future__ import division
import math
#initializing the variables:
Rf = 150;# in Ohms
Ra = 0.4;# in Ohms
I = 30;# in Amperes
V = 240;# in Volts
#calculation:
#Field current If
If = V/Rf
#Supply current I = Ia + If
#Hence armature current, Ia
Ia = I - If
#Back e.m.f. E = V - Ia*Ra
E = V - (Ia*Ra)
#Results
print "\n\n Result \n\n"
print "\n (a) current in the armature is ",round(Ia,2)," A "
print "\n (b) Back e.m.f. E is ",round(E,2)," V "
```

In [22]:

```
from __future__ import division
import math
#initializing the variables:
Ia1 = 30;# in Amperes
Ia2 = 45;# in Amperes
Ra = 0.4;# in ohm
n1 = 1350/60;# in Rev/sec
V = 200;# in Volts
#calculation:
#The relationship E proportional to (Phi*n) applies to both generators and motors. For a motor,
#E = V - (Ia*Ra)
E1 = V - (Ia1*Ra)
E2 = V - (Ia2*Ra)
#The relationship, E1/E2 = Phi1*n1/Phi2*n2, applies to both generators and motors.
#Since the flux is constant, Phi1 = Phi2
n2 = E2*n1/(E1)
#Results
print "\n\n Result \n\n"
print "\n the speed of the motor is ",round(n2,2)," rev/sec "
```

In [23]:

```
from __future__ import division
import math
#initializing the variables:
Ia1 = 30;# in Amperes
Ra = 0.4;# in ohm
n = 800/60;# in Rev/sec
V = 220;# in Volts
x= 0.1;
#calculation:
#For a d.c. shunt-wound motor, E = V - (Ia*Ra),Hence initial generated e.m.f.,
E1 = V - (Ia1*Ra)
#The generated e.m.f. is also such that E proportional to (Phi*n)
#so at the instant the flux is reduced, the speed has not had time to change, and
E = E1*(1-x)
#Hence, the voltage drop due to the armature resistance is
Vd = V - E
#The instantaneous value of the current is
Ia = Vd/Ra
#T proportional to (Phi*Ia), since the torque is constant,
#Phi1*Ia1 = Phi2*Ia2, The flux 8 is reduced by 10%, hence
Ia2 = Ia1/0.9
#Results
print "\n\n Result \n\n"
print "\n (a)instantaneous value of the current ",round(Ia,2)," A "
print "\n (b)steady state value of armature current, ",round(Ia2,2)," A "
```

In [3]:

```
from __future__ import division
import math
#initializing the variables:
Ia1 = 15;# in Amperes
Ia2 = 30;# in Amperes
Rf = 0.3;# in ohms
Ra = 0.2;# in ohm
n1 = 24;# in Rev/sec
V = 240;# in Volts
x= 2;
#calculation:
#generated e.m.f., E, at initial load, is given by
E1 = V - Ia1*(Ra + Rf)
#When the current is increased to 30 A, the generated e.m.f. is given by:
E2 = V - Ia2*(Ra + Rf)
#E proportional to (Phi*n)
#E1/E2 = Phi1*n1/Phi2*n2
n2 = E2*n1/(2*E1)
#Results
print "\n\n Result \n\n"
print "\n (a)generated e.m.f., E is ",round(E1,2)," V "
print "\n (b)speed of motor, n2, ",round(n2,2)," rev/sec "
```

In [25]:

```
from __future__ import division
import math
#initializing the variables:
I = 80;# in Amperes
C = 1500;# in Watt
Rf = 40;# in ohms
Ra = 0.2;# in ohm
n = 1000/60;# in Rev/sec
V = 320;# in Volts
#calculation:
#Field current, If
If = V/Rf
#Armature current Ia
Ia = I - If
#Efficiency
eff = ((V*I - (Ia*Ia*Ra) - (If*V) - C)/(V*I))*100 # in percent
#Results
print "\n\n Result \n\n"
print "\n efficiency is",round(eff,2),"%"
```

In [25]:

```
from __future__ import division
import math
#initializing the variables:
I = 40;# in Amperes
Rf = 0.05;# in ohms
Ra = 0.15;# in ohm
V = 250;# in Volts
#calculation:
#However for a series motor, If = 0 and the Ia*Ia*Ra loss needs to be I*I*(Ra + Rf)
#For maximum efficiency I*I*(Ra + Rf) = C
#Efficiency
eff = ((V*I - (2*I*I*(Ra + Rf)))/(V*I))*100 # in percent
#Results
print "\n\n Result \n\n"
print "\n efficiency is",round(eff,2)
```

In [26]:

```
from __future__ import division
import math
#initializing the variables:
T = 15;# in Nm
n = 1200/60;# in rev/sec
eff = 0.8;
V = 200;# in Volts
#calculation:
I = T*2*math.pi*n/(V*eff)
#Results
print "\n\n Result \n\n"
print "\n current supplied, I is ",round(I,2),"A"
```

In [27]:

```
from __future__ import division
import math
#initializing the variables:
R = 2;# in ohm
n = 30;# in rev/sec
I = 10;# in A
C = 300;# in Watt
V = 400;# in Volts
#calculation:
#Efficiency
eff = ((V*I - (I*I*R) - C)/(V*I))*100 # in percent
#Results
print "\n\n Result \n\n"
print "\n efficiency is",round(eff,2),"%"
```

In [2]:

```
from __future__ import division
import math
#initializing the variables:
Ia1 = 120;# in A
Ia2 = 60;# in A
Ra = 0.2;# in ohm
n1 = 10;# in rev/sec
R = 0.5;# in ohm
x = 0.8;
V = 500;# in Volts
#calculation:
#back e.m.f. at Ia1
E1 = V - Ia1*Ra
#at Ia2
E2 = V - Ia2*(Ra + R)
#E1/E2 = Phi1*n1/Phi2*n2
n2 = n1*E2/E1
#Back e.m.f. when Ia2
E3 = V - Ia2*Ra
n3 = n1*E3/(x*E1)
#Results
print "\n\n Result \n\n"
print "\n (a)speed n2 is ",round(n2,2)," rev/sec"
print "\n (b)speed n3 is ",round(n3,2)," rev/sec"
```

In [29]:

```
from __future__ import division
import math
#initializing the variables:
Ia1 = 90;# in Amperes
Ra = 0.1;# in ohm
Rse = 0.05;# in ohm
Rd = 0.2;# in Ohm
n1 = 15;# in rev/sec
V = 300;# in Volts
#calculation:
#e.m.f. E1
E1 = V - Ia1*(Ra + Rse)
#With the Rd diverter in parallel with Rse
#equivalent resistance, Re
Re = Rd*Rse/(Rd+Rse)
#Torque, T proprtional to Ia*Phi and for full load torque, Ia1*Phi1 = Ia2*Phi2
#Since flux is proportional to field current Phi1 proportional to Ta1 and Phi2 Proportional to I1
I1 = (Ia1*Ia1*0.8)**0.5
#By current division, current I1
Ia2 = I1/(Rd/(Rd + Rse))
#Hence e.m.f. E2
E2 = V - Ia2*(Ra + Re)
#E1/E2 = Phi1*n1/Phi2*n2
n2 = E2*Ia1*n1/(I1*E1)
#Results
print "\n\n Result \n\n"
print "\n speed n2 is ",round(n2,2)," rev/sec"
```

In [30]:

```
from __future__ import division
import math
#initializing the variables:
Ia1 = 25;# in Amperes
Ra = 0.4;# in ohm
Rse = 0.2;# in ohm
n1 = 800/60;# in rev/sec
n2 = 600/60;# in rev/sec
V = 400;# in Volts
#calculation:
#e.m.f. E1
E1 = V - Ia1*(Ra + Rse)
#At n2, since the current is unchanged, the flux is unchanged.
#E1/E2 = n1/n2
E2 = E1*n2/n1
#and E2 = V - Ia1(Ra + Rse + R)
R = (V - E2)/Ia1 - Ra - Rse
#Results
print "\n\n Result \n\n"
print "\n Resistance is ",round(R,2)," ohm"
```