Solution:

Given data:
Resistance per phase (Rotor resistance), Rr = 0.04 ohm
Reactance per phase (Standstill reactance), Xs = 0.2 ohm
External resistance, Re = 0.02 ohm

To find:
Percentage improvement in power factor during starting.

Let's analyze the circuit and calculate the power factor in two cases: without the external resistance and with the external resistance.

1. Without the external resistance:
In the absence of the external resistance, the circuit can be represented as follows:

|---------|
V | |
-----> | |
| |
| |
| Rr | Xs
| |
| |
|---------|

The power factor in this case can be calculated using the formula:

power factor (cosφ) = Rr / √(Rr² + Xs²)

power factor (cosφ) = 0.04 / √(0.04² + 0.2²)

power factor (cosφ) = 0.04 / √(0.0016 + 0.04)

power factor (cosφ) = 0.04 / √0.0416

power factor (cosφ) = 0.04 / 0.204

power factor (cosφ) ≈ 0.196

2. With the external resistance:
When the external resistance is added to the circuit, the circuit can be represented as follows:

|---------|
V | |
-----> | |
| |
| |
| Rr | Xs
| |
| |
|---------|
| |
| |
| |
| |
| Re |
| |
| |
|---------|

The power factor in this case can be calculated using the formula:

power factor (cosφ') = (Rr + Re) / √((Rr + Re)² + Xs²)

power factor (cosφ') = (0.04 + 0.02) / √((0.04 + 0.02)² + 0.2²)

power factor (cosφ') = 0.06 / √(0.0016 + 0.0004 + 0.04 + 0.0004)

power factor (cosφ') = 0.06 / √0.0424

power factor (cosφ') = 0.06 / 0.206

power factor (cosφ') ≈ 0.291

Now, let's calculate the percentage improvement in power factor during starting:

Percentage improvement = [(cosφ' - cosφ) / cosφ] x 100

Percentage improvement = [(0.291 - 0.196) / 0.196] x 100

Percentage improvement = (0.095 / 0.196) x 100

Percentage improvement ≈ 48.47%

Therefore, the percentage improvement in power factor during starting, when the external resistance of 0.02 ohm is added, is approximately 46.60%. Hence, the correct

Given: R₂ = 0.04Ω