Reducing Starting Current in a DC Motor with External Resistances

Introduction:
In a DC motor, the starting current can be quite high, which can lead to excessive power consumption and potential damage to the motor. To reduce the starting current, external resistances are often used in the armature and field circuits of the motor. The question asks which combination of resistance values would be most effective in reducing the starting current.

Explanation:
To understand the answer, let's analyze the effect of the resistance values in both the armature and field circuits on the starting current.

1. Armature Circuit Resistance (Ra):
The armature circuit resistance, Ra, limits the flow of current through the armature winding. A higher resistance in the armature circuit will reduce the current flowing through it.

2. Field Circuit Resistance (Rf):
The field circuit resistance, Rf, affects the strength of the magnetic field produced by the field winding. A higher resistance in the field circuit will reduce the field current and therefore the strength of the magnetic field.

Now, let's examine the effect of different resistance combinations on the starting current:

a) Ra is maximum and Rf is minimum:
- When Ra is maximum, it effectively limits the armature current, reducing the starting current.
- When Rf is minimum, a stronger magnetic field is produced, which can help in reducing the starting current.
- This combination provides the most effective reduction in the starting current.

b) Rf is maximum and Ra is minimum:
- When Rf is maximum, it drastically reduces the field current, leading to a weaker magnetic field.
- When Ra is minimum, it allows a higher armature current, increasing the starting current.
- This combination does not effectively reduce the starting current.

c) Ra is minimum and Rf is minimum:
- When Ra is minimum, it allows a higher armature current, increasing the starting current.
- When Rf is minimum, a weaker magnetic field is produced, which does not help in reducing the starting current.
- This combination does not effectively reduce the starting current.

d) Ra is maximum and Rf is maximum:
- When Ra is maximum, it effectively limits the armature current, reducing the starting current.
- When Rf is maximum, it drastically reduces the field current, leading to a weaker magnetic field.
- This combination does not effectively reduce the starting current.

Conclusion:
Among the given options, the combination of Ra being maximum and Rf being minimum is the most effective in reducing the starting current in a DC motor. This combination limits the armature current while providing a strong magnetic field, resulting in a significant reduction in the starting current.