In [1]:

```
import math
import cmath
#Variable declaration
hp = 0.25 #Power rating of the single-phase motor(hp)
V = 110.0 #Voltage rating of the single-phase motor(V)
I_sw = 4.0 #Starting winding current(A)
phi_I_sw = 15.0 #Phase angle by which I_sw lags behind V(degree)
I_rw = 6.0 #Running winding current(A)
phi_I_rw = 40.0 #Phase angle by which I_rw lags behind V(degree)
#Calculation
#Case(a)
I_s = I_sw*cmath.exp(1j*-phi_I_sw*math.pi/180) #Starting current(A)
I_r = I_rw*cmath.exp(1j*-phi_I_rw*math.pi/180) #Running current(A)
I_t = I_s+I_r #Total starting current(A)
I_t_angle = cmath.phase(I_t)*180/math.pi #Angle of total starting current(degree)
Power_factor = math.cos(I_t_angle*math.pi/180) #Power factor
#Case(b)
Is_cos_theta = I_s.real #Component of starting winding current in phase with the supply voltage(A)
#Case(c)
Ir_sin_theta = I_r.imag #Component of running winding current that lags the supply voltage by 90°(A)
#Case(d)
phase = (phi_I_rw-phi_I_sw) #Phase angle between the starting and running currents(degree)
#Result
print('Case(a): Total starting current , I_t = %.2f∠%.f° A' %(abs(I_t),I_t_angle))
print(' Power factor = %.3f lagging' %Power_factor)
print('Case(b): Component of starting winding current in phase with the supply voltage , I_s*cosθ = %.2f A' %Is_cos_theta)
print('Case(c): Component of running winding current that lags the supply voltage by 90° , I_r*sinθ = %.2fj A' %Ir_sin_theta)
print('Case(d): Phase angle between starting and running currents , (θ_r-θ_s) = %.f° ' %phase)
```

In [1]:

```
import math
#Variable declaration
hp = 0.25 #Power rating of the single-phase motor(hp)
V = 110.0 #Voltage rating of the single-phase motor(V)
I_s = 4.0 #Starting winding current(A)
phi_I_s = 15.0 #Phase angle by which I_sw lags behind V(degree)
I_r = 6.0 #Running winding current(A)
phi_I_r = 40.0 #Phase angle by which I_rw lags behind V(degree)
#Calculation
P_s = V*I_s*math.cos(phi_I_s*math.pi/180) #Power dissipated by starting winding(W)
P_r = V*I_r*math.cos(phi_I_r*math.pi/180) #Power dissipated in the running winding(W)
P_t = P_s+P_r #Total instantaneous power dissipated during starting(W)
P_r_d = P_r #Total steady-state power dissipated during running(W)
n = hp*746/P_r*100 #Efficiency(%)
#Result
print('Case(a): Power dissipated by the starting winding , P_s = %.f W' %P_s)
print('Case(b): Power dissipated in the running winding , P_r = %.1f W' %P_r)
print('Case(c): Total instantaneous power dissipated during starting , P_t = %.1f W' %P_t)
print('Case(d): Total steady-state power dissipated during running , P_r = %.1f W' %P_r_d)
print('Case(e): Motor efficiency , η = %.f percent' %n)
```

In [1]:

```
import math
import cmath
#Variable declaration
hp = 0.25 #Power rating of the single-phase motor(hp)
V = 110.0 #Voltage rating of the single-phase motor(V)
I_sw = 4.0 #Starting winding current(A)
phi_I_sw = 42.0 #Phase angle by which I_sw lead V(degree)
I_rw = 6.0 #Running winding current(A)
phi_I_rw = 40.0 #Phase angle by which I_rw lags behind V(degree)
#Calculation
#Case(a)
I_s = I_sw*cmath.exp(1j*phi_I_sw*math.pi/180) #Starting current(A)
I_r = I_rw*cmath.exp(1j*-phi_I_rw*math.pi/180) #Running current(A)
I_t = I_s+I_r #Total starting current(A)
I_t_angle = cmath.phase(I_t)*180/math.pi #Angle of total starting current(degree)
Power_factor = math.cos(I_t_angle*math.pi/180) #Power factor
#Case(b)
angle = (phi_I_rw-(-phi_I_sw)) #Angle between starting and running current(degree)
sin_angle = math.sin(angle*math.pi/180) #Sine of the angle between starting and running currents
#Case(c)
T_ratio = sin_angle/math.sin(25*math.pi/180) #Ratio of starting torque
#Result
print('Case(a): Total starting current , I_t = %.2f∠%.1f° A' %(abs(I_t),I_t_angle))
print(' Power factor = %.3f ' %Power_factor)
print('Case(b): Sine of the angle between starting and running currents = %.4f ' %sin_angle)
print('Case(c): Steady state starting current has been reduced from 9.88∠-30° A to %.2f∠%.1f° A' %(abs(I_t),I_t_angle))
print(' The power factor has raised from 0.866 lagging to %.3f' %Power_factor)
print(' The ratio of starting torques , T_cs/T_rs = %.2f ' %T_ratio)
```

In [1]:

```
#Variable declaration
T_r = 1.0 #Rated torque(lb-ft)
P_in = 400.0 #Rated input power(W)
V = 115.0 #Rated input voltage(V)
I_t = 5.35 #Rated input current(A)
Speed = 1750.0 #Rated speed(rpm)
hp = 1.0/3 #Rated hp
T_s = 4.5 #Starting torque(lb-ft) From Locked-Rotor data
T_br = 2.5 #Breakdown torque(lb-ft) From Breakdown-Torque data
#Calculation
T_s_r = T_s/T_r #Ratio of starting to rated torque
T_br_r = T_br/T_r #Ratio of breakdown to rated torque
P_o = hp*746 #Power output(W)
n = P_o/P_in*100 #Rated load efficiency(%)
S = V*I_t #VA rating of the motor
cos_theta = P_in/S #Rated load power factor
hp = T_r*Speed/5252 #Rated load horsepower
#Result
print('Case(a): Ratio of starting to rated torque , T_s/T_r = %.1f ' %T_s_r)
print('Case(b): Ratio of breakdown to rated torque , T_br/T_r = %.1f ' %T_br_r)
print('Case(c): Rated load efficiency , η = %.1f percent' %n)
print('Case(d): Rated load power factor , cosθ = %.4f ' %cos_theta)
print('Case(e): Rated load horsepower , hp = %.4f hp' %hp)
```