In [1]:

```
#Variable declaration
V = 525.0 #Voltage of motor(V)
I_1 = 50.0 #Current(A)
T_1 = 216.0 #Torque(N-m)
I_2 = 70.0 #Current(A)
T_2 = 344.0 #Torque(N-m)
I_3 = 80.0 #Current(A)
T_3 = 422.0 #Torque(N-m)
I_4 = 90.0 #Current(A)
T_4 = 500.0 #Torque(N-m)
V_m = 26.0 #Speed(kmph)
R_b = 5.5 #Resistance of braking rheostat(ohm)
R_m = 0.5 #Resistance of motor(ohm)
#Calculation
I = 75.0 #Current drawn at 26 kmph(A)
back_emf = V-I*R_m #Back emf of the motor(V)
R_t = R_b+R_m #Total resistance(ohm)
I_del = back_emf/R_t #Current delivered(A)
T_b = T_3*I_del/I_3 #Braking torque(N-m)
#Result
print('Braking torque = %.f N-m' %T_b)
```

In [1]:

```
#Variable declaration
V = 525.0 #Voltage of motor(V)
I_1 = 50.0 #Current(A)
N_1 = 1200.0 #Speed(rpm)
I_2 = 100.0 #Current(A)
N_2 = 950.0 #Speed(rpm)
I_3 = 150.0 #Current(A)
N_3 = 840.0 #Speed(rpm)
I_4 = 200.0 #Current(A)
N_4 = 745.0 #Speed(rpm)
N = 1000.0 #Speed opearting(rpm)
R = 3.0 #Resistance(ohm)
R_m = 0.5 #Resistance of motor(ohm)
#Calculation
I = 85.0 #Current drawn at 1000 rpm(A)
back_emf = V-I*R_m #Back emf of the motor(V)
R_t = R+R_m #Total resistance(ohm)
I_del = back_emf/R_t #Current delivered(A)
#Result
print('Current delivered when motor works as generator = %.f A' %I_del)
```

In [1]:

```
#Variable declaration
W = 400.0 #Weight of train(tonne)
G = 100.0/70 #Gradient(%)
t = 120.0 #Time(sec)
V_1 = 80.0 #Speed(km/hr)
V_2 = 50.0 #Speed(km/hr)
r_kg = 5.0 #Tractive resistance(kg/tonne)
I = 7.5 #Rotational inertia(%)
n = 0.75 #Overall efficiency
#Calculation
W_e = W*(100+I)/100 #Accelerating weight of train(tonne)
r = r_kg*9.81 #Tractive resistance(N-m/tonne)
energy_recuperation = 0.01072*W_e*(V_1**2-V_2**2)/1000 #Energy available for recuperation(kWh)
F_t = W*(r-98.1*G) #Tractive effort during retardation(N)
distance = (V_1+V_2)*1000*t/(2*3600) #Distance travelled by train during retardation period(m)
energy_train = abs(F_t)*distance/(3600*1000) #Energy available during train movement(kWh)
net_energy = n*(energy_recuperation+energy_train) #Net energy returned to supply system(kWh)
#Result
print('Energy returned to lines = %.2f kWh' %net_energy)
print('\nNOTE: ERROR: Calculation mistakes & more approximation in textbook solution')
```

In [1]:

```
#Variable declaration
W = 355.0 #Weight of train(tonne)
V_1 = 80.5 #Speed(km/hr)
V_2 = 48.3 #Speed(km/hr)
D = 1.525 #Distance(km)
G = 100.0/90 #Gradient(%)
I = 10.0 #Rotational inertia(%)
r = 53.0 #Tractive resistance(N/tonne)
n = 0.8 #Overall efficiency
#Calculation
beta = (V_1**2-V_2**2)/(2*D*3600) #Braking retardation(km phps)
W_e = W*(100+I)/100 #Accelerating weight of train(tonne)
F_t = 277.8*W_e*beta+98.1*W*G-W*r #Tractive effort(N)
work_done = F_t*D*1000 #Work done by this effort(N-m)
energy = work_done*n/(1000*3600) #Energy returned to line(kWh)
#Result
print('Energy returned to the line = %.1f kWh' %energy)
```

In [1]:

```
import math
#Variable declaration
area = 16.13 #Area of brakes(sq.cm/pole face)
phi = 2.5*10**-3 #Flux(Wb)
u = 0.2 #Co-efficient of friction
W = 10.0 #Weight of car(tonnes)
#Calculation
a = area*10**-4 #Area of brakes(sq.m/pole face)
F = phi**2/(2*math.pi*10**-7*a) #Force(N)
beta = u*F/(W*1000)*100 #Beta(cm/sec^2)
#Result
print('Braking effect, β = %.2f cm/sec^2' %beta)
```