In [1]:

```
#Question:
"""Finding the slip and efficiency of induction motor."""
#Variable Declaration:
f=50 #Frequency rating of the induction motor(in Hertz)
P=4 #Number of poles in the induction motor
N=1410 #Speed of the motor(in rpm)
Po=375 #Output Power(in Watts)
V=230 #Voltage rating of the induction motor(in Volts)
I=2.9 #Input current(in Amperes)
pf=0.71 #Power factor(lagging)
#Calculations:
Ns=(120.0*f)/P
slip=(Ns-N)/Ns
#Result:
print "Slip is %.2f percent." %(slip*100)
Pin=V*I*pf
efficiency=Po/Pin
print "The efficiency is %.2f percent." %(efficiency*100)
```

In [2]:

```
#Question:
"""Finding the currents and the power factor in the induction motor."""
from cmath import phase,rect,polar
from math import radians,degrees,cos
#Variable Declartion:
V=rect(230,0) #Voltage rating of the split-phase induction motor(in Volts)
Z_M=5+ 12*1j #Impedance of the main winding(in Ohms)
Z_A=12+ 5*1j #Start-winding impedance(in Ohms)
#Calculations:
mod_Z_M=abs(Z_M)
mod_Z_A=abs(Z_A)
phi_M=phase(Z_M)
phi_A=phase(Z_A)
I_M=V/Z_M
mod_I_M=abs(I_M)
phi_I_M=degrees(phase(I_M))
I_A=V/Z_A
mod_I_A=abs(I_A)
phi_I_A=degrees(phase(I_A))
I_L=I_M+I_A
mod_I_L=abs(I_L)
phi_I_L=degrees(phase(I_L))
phi=phi_I_A-phi_I_M
pf=cos(radians(phi_I_L))
#Result:
print "(a)The current in the main winding is %.2f A at a phase angle of %.2f degrees." %(mod_I_M,phi_I_M)
print "(b)The current in the starting winding is %.2f A at a phase angle of %.2f degrees." %(mod_I_A,phi_I_A)
print "(c)The line current is %.2f A at a phase angle of %.2f degrees." %(mod_I_L,phi_I_L)
print "(d)The phase displacement between the two winding currents is %.2f degrees." %(phi)
print "(e)The power factor is %.4f lagging." %(pf)
```

In [3]:

```
#Question:
"""Finding the capacitance in series with the auxiliary winding to maximize starting torque."""
from math import radians,degrees,atan,pi,tan
#Variable Declaration:
X_M=20 #Inductive reactance of the main winding(in Ohm)
R_M=2 #Resistance of the main winding(in Ohm)
X_A=5 #Inductive reactance of the auxiliary winding(in Ohm)
R_A=25 #Resistance of the auxiliary winding(in Ohm)
f=50 #Frequency rating of the split-phase induction motor(in Hertz)
#Calculations:
angle_M=atan(X_M/R_M)
angle_A=degrees(angle_M)-90
Xc=X_A-(R_A*tan(radians(angle_A)))
#Result:
C=1/(2*pi*f*Xc)
print "The value of capacitance connected in series with the auxiliary winding to obtain maximum starting torque is %e F." %(C)
```

In [6]:

```
#Question:
"""Finding the resolution and shaft speed of a stepper motor."""
#Variable Declaration:
beta=2.5 #Step-angle of a stepper motor(in degrees)
step_freq=3600 #Stepping frequency(in pps)
#Calculations:
res=360/beta
number_steps=res*25
shaft_speed=(beta*step_freq)/360
#Result:
print "(a)The resolution is %d steps per revolution." %(res)
print "(b)The number of steps required for the shaft to make 25 revolutions=%d." %(number_steps)
print "(c)The shaft speed is %.2f rps." %(shaft_speed)
```

In [7]:

```
#Question:
"""Finding the number of stator and rotor poles in a VR motor."""
#Variable Declaration:
m=3 #Number of phases
beta=15 #Step angle(in degrees)
#Calculations:
Nr=360/(m*beta)
Ns1=(Nr*360)/(360-(beta*Nr))
Ns2=(Nr*360)/(360+(beta*Nr))
#Result:
print "(a) The number of rotor poles is %d." %(Nr)
print "(b)"
print " Case 1: Ns>Nr"
print " The number of stator poles is %d. \n" %(Ns1)
print " Case 2: Ns<Nr"
print " The number of stator poles is %d." %(Ns2)
```

In [8]:

```
#Question:
"""Finding the number of rotor and stator teeth in VR stepper motor."""
#Variable Declaration:
m=4 #Number of stacks
beta=1.8 #Step angle(in degrees)
#Calculations:
Nr=360/(m*beta)
Ns=Nr
#Result:
print "The number of rotor teeth is %d." %(Nr)
print "The number of stator teeth is %d." %(Ns)
print "\nNOTE: In a multistack stepper motor the number of stator teeth is same as that of the rotor teeth."
```