In [1]:

```
#Variable declaration
t = 50.0*10**-3 #Time(second)
phi = 8.0*10**6 #Uniform magnetic field(maxwells)
#Calculation
E_av = (phi/t)*10**-8 #Average voltage generated in the conductor(V)
#Result
print('Average voltage generated in the conductor , E_av = %.1f V' %E_av)
```

In [1]:

```
#Variable declaration
l = 18.0 #Length of the conductor(inches)
B = 50000.0 #Uniform magnetic field(lines/sq.inches)
d = 720.0 #Distance travelled by conductor(inches)
t = 1.0 #Time taken for the conductor to move(second)
#Calculation
#Case(a)
v = d/t #Velocity with which the conductor moves(inches/second)
e = B*l*v*10**-8 #Instantaneous induced EMF(V)
#Case(b)
A = d*l #Area swept by the conductor while moving(sq.inches)
phi = B*A #Uniform magnetic field(lines)
E = (phi/t)*10**-8 #Average induced EMF(V)
#Result
print('Case(a): Instantaneous induced EMF , e = %.2f V' %e)
print('Case(b): Average induced EMF , E = %.2f V' %E)
```

In [1]:

```
import math
#Variable declaration
l = 18.0 #Length of the conductor(inches)
B = 50000.0 #Uniform magnetic field(lines/sq.inches)
d = 720.0 #Distance travelled by conductor(inches)
t = 1.0 #Time taken for the conductor to move(second)
theta = 75.0 #Angle between the motion of the conductor and field(degree)
#Calculation
v = d/t #Velocity with which the conductor moves(inches/second)
E = B*l*v*math.sin(theta*math.pi/180)*10**-8 #Instantaneous induced voltage(V)
#Result
print('Average induced voltage , E = %.2f V' %E)
```

In [1]:

```
import math
#Variable declaration
v = 1.5 #Velocity of moving conductor(m/s)
l = 0.4 #Length of the conductor(m)
B = 1 #Uniform field(tesla)
theta_a = 90.0 #Angle between the motion of the conductor and field(Degree)
theta_b = 35.0 #Angle between the motion of the conductor and field(Degree)
theta_c = 120.0 #Angle between the motion of the conductor and field(Degree)
#Calculation
E_a = B*l*v*math.sin(theta_a*math.pi/180) #Voltage induced in the conductor(V)
E_b = B*l*v*math.sin(theta_b*math.pi/180) #Voltage induced in the conductor(V)
E_c = B*l*v*math.sin(theta_c*math.pi/180) #Voltage induced in the conductor(V)
#Result
print('Case(a): Voltage induced in the conductor , E = %.1f V' %E_a)
print('Case(b): Voltage induced in the conductor , E = %.3f V' %E_b)
print('Case(c): Voltage induced in the conductor , E = %.2f V' %E_c)
```

In [1]:

```
#Variable declaration
no_of_conductors = 40.0 #Number of conductors
A = 2.0 #Number of parallel paths
path = A
flux_per_pole = 6.48*10**8 #Flux per pole(lines)
N = 30.0 #Speed of the prime mover(rpm)
R_per_path = 0.01 #Resistance per path
I = 10.0 #Current carrying capacity of each conductor(A)
P = 2.0 #Number of poles
#Calculation
phi_T = P*flux_per_pole #Total flux linked in one revolution(lines)
t = (1/N)*(60) #Time for one revolution(s/rev)
#Case(a)
e_av_per_conductor = (phi_T/t)*10**-8 #Average voltage generated(V/conductor)
E_per_path = (e_av_per_conductor)*(no_of_conductors/path) #Average voltage generated(V/path)
#Case(b)
E_g = E_per_path #Generated armature voltage(V)
#Case(c)
I_a = (I/path)*(2*path) #Armature current delivered to an external load(A)
#Case(d)
R_a = (R_per_path)/path*(no_of_conductors/P) #Armature resistance(ohm)
#Case(e)
V_t = E_g-(I_a*R_a) #Terminal voltage of the generator(V)
#Case(f)
P = V_t*I_a #Generator power rating(W)
#Result
print('Case(a): Average voltage generated per path , E/path = %.1f V/path' %E_per_path)
print('Case(b): Generated armature voltage , E_g = %.1f V' %E_g)
print('Case(c): Armature current delivered to an external load , I_a = %.f A' %I_a)
print('Case(d): Armature resistance , R_a = %.1f Ω' %R_a)
print('Case(e): Terminal voltage of the generator , V_t = %.1f V' %V_t)
print('Case(f): Generator power rating , P = %.f W' %P)
```

In [1]:

```
#Variable declaration
no_of_conductors = 40.0 #Number of conductors
path = 4.0 #Number of parallel paths
flux_per_pole = 6.48*10**8 #Flux per pole(lines)
N = 30.0 #Speed of the prime mover(rpm)
R_per_path = 0.01 #Resistance per path
I = 10.0 #Current carrying capacity of each conductor(A)
P = 4.0 #Number of poles
#Calculation
phi_T = 2*flux_per_pole #Total flux linked in one revolution(lines). From Example 1.5
t = (1/N)*(60) #Time for one revolution(s/rev)
#Case(a)
e_av_per_conductor = (phi_T/t)*10**-8 #Average voltage generated(V/conductor)
E_per_path = (e_av_per_conductor)*(no_of_conductors/path) #Average voltage generated(V/path)
#Case(b)
E_g = E_per_path #Generated armature voltage(V)
#Case(c)
I_a = (I/path)*(4*path) #Armature current delivered to an external load(A)
#Case(d)
R_a = (R_per_path)/path*(no_of_conductors/P) #Armature resistance(ohm)
#Case(e)
V_t = E_g-(I_a*R_a) #Terminal voltage of the generator(V)
#Case(f)
P = V_t*I_a #Generator power rating(W)
#Result
print('Case(a): Average voltage generated per path , E/path = %.1f V/path' %E_per_path)
print('Case(b): Generated armature voltage , E_g = %.1f V' %E_g)
print('Case(c): Armature current delivered to an external load , I_a = %.f A' %I_a)
print('Case(d): Armature resistance , R_a = %.3f Ω' %R_a)
print('Case(e): Terminal voltage of the generator , V_t = %.1f V' %V_t)
print('Case(f): Generator power rating , P = %.f W' %P)
```

In [1]:

```
#Variable declaration
N = 1.0 #Number of turns
phi = 6.48*10**8 #Magnetic flux(lines)
rpm = 30.0 #Number of revolution
s = rpm/60 #Number of revolution of the coil per second(rev/s)
#Calculation
E_av_per_coil = 4*phi*N*s*10**-8 #Average voltage per coil(V/coil)
E_av_per_coil_side = E_av_per_coil*(1.0/2) #Average voltage per conductor(V/conductor)
#Result
print('Case(a): Average voltage per coil , E_av/coil = %.2f V/coil' %E_av_per_coil)
print('Case(b): Average voltage per conductor , E_av/coil side = %.2f V/conductor' %E_av_per_coil_side)
```

In [1]:

```
import math
#Variable declaration
N = 1.0 #Number of turns
phi_lines = 6.48*10**8 #Magnetic flux(lines/pole)
rpm = 30.0 #Number of revolution per second
s = rpm/60 #Number of revolution of the coil per second(rev/s)
#Calculation
phi = phi_lines*10**-8 #Magnetic flux(Wb)
omega = rpm*2*math.pi*(1.0/60) #Angular velocity(rad/s)
E_av_per_coil = 0.63662*omega*phi*N #Average voltage per coil(V/coil)
#Result
print('Average voltage per coil , E_av/coil = %.2f V/coil' %E_av_per_coil)
```

In [1]:

```
#Variable declaration
P = 2.0 #Number of poles
Z = 40.0 #Number of conductors
a = 2.0 #Parallel paths
phi = 6.48*10**8 #Magnetic flux(lines/pole)
S = 30.0 #Speed of the prime mover
#Calculation
E_g = (phi*Z*S*P)/(60*a)*10**-8 #Average voltage between the brushes(V)
#Result
print('Average voltage between the brushes , E_g = %.1f V' %E_g)
```

In [1]:

```
import math
#Variable declaration
no_of_coils = 40.0 #Number of coils
N = 20.0 #Number of turns in each coil
omega = 200.0 #Angular velocity of armature(rad/s)
phi = 5.0*10**-3 #Flux(Wb/pole)
a = 4.0 #Number of parallel paths
P = 4.0 #Number of poles
#Calculation
Z = no_of_coils*2.0*N #Number of conductors
E_g = (phi*Z*omega*P)/(2*math.pi*a) #Voltage generated by the armature between brushes(V)
#Result
print('Case(a): Number of conductors , Z = %.f conductors' %Z)
print('Case(b): Voltage between brushes generated by the armature , E_g = %.1f V' %E_g)
```

In [1]:

```
#Variable declaration
l = 0.5 #Length of the conductor(m)
A = 0.1*0.2 #Area of the pole face(sq.meter)
phi = 0.5*10**-3 #Magnetic flux(Wb)
I = 10.0 #Current in the conductor(A)
#Calculation
B = phi/A #Flux density(Wb/m^2)
F = B*I*l*1000 #Magnitude of force(mN)
#Result
print('Case(a): Magnitude of the force , F = %.f mN' %F)
print('Case(b): The direction of the force on the conductor is %.f mN in an upward direction' %F)
```

In [1]:

```
import math
#Variable declaration
l = 0.5 #Length of the conductor(m)
A = 0.1*0.2 #Area of the pole face(sq.meter)
phi = 0.5*10**-3 #Magnetic flux(Wb)
I = 10.0 #Current in the conductor(A)
theta = 75.0 #Angle between the conductor and the flux density(degree)
#Calculation
B = phi/A #Flux density(Wb/m^2)
F = B*I*l*math.sin(theta*math.pi/180)*1000 #Magnitude of force(mN)
#Result
print('Magnitude of the force , F = %.2f mN in an vertically upward direction' %F)
```

In [1]:

```
#Variable declaration
R_a = 0.25 #Armature resistance(ohm)
V_a = 125.0 #DC bus voltage(V)
I_a = 60.0 #Armature current(A)
#Calculation
E_c = V_a-(I_a*R_a) #Counter EMF generated in the armature conductors of motor(V)
#Result
print('Counter EMF generated in the armature conductors of motor , E_c = %.f V' %E_c)
```

In [1]:

```
#Variable declaration
V_a = 110.0 #Voltage across armature(V)
I_a = 60.0 #Armature current(A)
R_a = 0.25 #Armature resistance(ohm)
P = 6.0 #Number of poles
a = 12.0 #Number of paths
Z = 720.0 #No. of armature conductors
S = 1800.0 #Speed(rpm)
#Calculation
E_g = V_a+(I_a*R_a) #Generated EMF in the armature(V)
phi_lines = E_g*60*a/(Z*S*P*10**-8) #Flux per pole in lines(lines/pole)
phi_mWb = phi_lines*10**-8*1000 #Flux per pole milliwebers(mWb)
#Result
print('Case(a): Generated EMF in the armature , E_g = %.f V' %E_g)
print('Case(b): Flux per pole in lines , Φ = %.2e lines/pole' %phi_lines)
print('Case(c): Flux per pole milliwebers , Φ = %.1f mWb' %phi_mWb)
```