Introduction:
In this question, we are given a 3-phase induction motor with a maximum torque to full-load torque ratio of 2:1. We need to determine the ratio of actual starting torque to full-load torque for Y-Δ starting. The motor parameters given are R2 = 0.2 Ω and X2 = 2 Ω.

Solution:

Step 1: Calculate the starting torque
The starting torque of an induction motor can be calculated using the following formula:

Starting Torque (Ts) = (3 * V^2 * R2) / (s * (R2^2 + X2^2))

Where,
V is the rated voltage
R2 is the rotor resistance
X2 is the rotor reactance
s is the slip

Step 2: Calculate the full-load torque
The full-load torque of an induction motor can be calculated using the following formula:

Full-Load Torque (Tf) = (3 * V^2) / (ωs * (R2^2 + X2^2))

Where,
V is the rated voltage
ωs is the synchronous speed of the motor

Step 3: Calculate the ratio of starting torque to full-load torque for Y-Δ starting
The ratio of actual starting torque to full-load torque for Y-Δ starting can be calculated using the following formula:

Ratio = Ts / Tf

Step 4: Substituting the given values in the formulas
Given that the maximum torque to full-load torque ratio is 2:1, we can write:

Tmax / Tf = 2 / 1

Since the maximum torque occurs at slip s = 1, we can calculate the value of Tmax using the formula for starting torque:

Tmax = (3 * V^2 * R2) / (1 * (R2^2 + X2^2))

Substituting the given values of R2 = 0.2 Ω and X2 = 2 Ω, we can calculate Tmax.

Similarly, we can calculate the full-load torque Tf using the given values of V and ωs.

Step 5: Calculate the ratio of actual starting torque to full-load torque
Once we have the values of Tmax and Tf, we can calculate the ratio of actual starting torque to full-load torque using the formula:

Ratio = Tmax / Tf

Substituting the calculated values of Tmax and Tf, we can find the required ratio.

Conclusion:
In this question, we calculated the ratio of actual starting torque to full-load torque for Y-Δ starting in a 3-phase induction motor. We used the formulas for starting torque and full-load torque, and substituted the given values to calculate the required ratio.