# CHAPTER 1: ELECTROMECHANICAL FUNDAMENTALS¶

## Example 1.1, Page number 5¶

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)

Average voltage generated in the conductor , E_av = 1.6 V


## Example 1.2, Page number 6¶

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)

Case(a): Instantaneous induced EMF , e = 6.48 V
Case(b): Average induced EMF , E = 6.48 V


## Example 1.3, Page number 8¶

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)

Average induced voltage , E = 6.26 V


## Example 1.4, Page number 9¶

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)

Case(a): Voltage induced in the conductor , E = 0.6 V
Case(b): Voltage induced in the conductor , E = 0.344 V
Case(c): Voltage induced in the conductor , E = 0.52 V


## Example 1.5, Page number 19¶

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)

Case(a): Average voltage generated per path , E/path = 129.6 V/path
Case(b): Generated armature voltage , E_g = 129.6 V
Case(c): Armature current delivered to an external load , I_a = 20 A
Case(d): Armature resistance , R_a = 0.1 Ω
Case(e): Terminal voltage of the generator , V_t = 127.6 V
Case(f): Generator power rating , P = 2552 W


## Example 1.6, Page number 20¶

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)

Case(a): Average voltage generated per path , E/path = 64.8 V/path
Case(b): Generated armature voltage , E_g = 64.8 V
Case(c): Armature current delivered to an external load , I_a = 40 A
Case(d): Armature resistance , R_a = 0.025 Ω
Case(e): Terminal voltage of the generator , V_t = 63.8 V
Case(f): Generator power rating , P = 2552 W


## Example 1.7, Page number 23¶

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)

Case(a): Average voltage per coil , E_av/coil = 12.96 V/coil
Case(b): Average voltage per conductor , E_av/coil side = 6.48 V/conductor


## Example 1.8, Page number 23¶

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)
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)

Average voltage per coil , E_av/coil  = 12.96 V/coil


## Example 1.9, Page number 24¶

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)

Average voltage between the brushes , E_g = 129.6 V


## Example 1.10, Page number 24¶

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)

Case(a): Number of conductors , Z = 1600 conductors
Case(b): Voltage between brushes generated by the armature , E_g = 254.6 V


## Example 1.11, Page number 26¶

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)

Case(a): Magnitude of the force , F = 125 mN
Case(b): The direction of the force on the conductor is 125 mN in an upward direction


## Example 1.12, Page number 26¶

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)

Magnitude of the force , F = 120.74 mN in an vertically upward direction


## Example 1.13, Page number 29¶

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)

Counter EMF generated in the armature conductors of motor , E_c = 110 V


## Example 1.14, Page number 29¶

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)

Case(a): Generated EMF in the armature , E_g = 125 V
Case(b): Flux per pole in lines , Φ = 1.16e+06 lines/pole
Case(c): Flux per pole milliwebers , Φ = 11.6 mWb