Quick transformer regulation question - Please help

[MRSquared]

Homework Statement

Tests are performed on a 50Hz transformer which yield the following results:
Short circuit test: V₁ = 40V, I₁ = 10A, Power input = 20W
Open circuit test: V₁ = 240V, I₁ = 1.2A, Power input = 70W

Here are the equivalent circuit parameters from the above tests.
R_c = 823 Ω, (R₁ + R₂') = 0.2 Ω, (l₁ + l₂') = 12.7mH, L_m = 0.656H

Determine the regulation of the transformer (using the approximate equivalent cct), assuming that the rated primary voltage is 240V (50Hz) and that the rated secondary current referred to the primary is 10A. (Assume pure resistive load).

Homework Equations

Per unit voltage regulation = $$\frac{{{V_{{\rm{sc}}}}\cos \left( {{\phi _e} - {\phi _2}} \right)}}{{{V_1}}}$$

The Attempt at a Solution

This is the problem given by my lecturer. My textbook says the voltage regulation can be calculated using the above formula from the short circuit test. I'm now going to substitute the variables into the equation.
V_sc = 40 V (from short-circuit test)
Φ_c = 0.243 (calculated)
V₁ = 240 V (given)
Φ₂ = ?

From all the examples I've seen, Φ₂ is given. Am I missing something or there's a problem with the question? Thank you in advance.

 

[KataKoniK]

Thank you for sharing your problem with us. After reviewing the information provided, it seems that there may be an error in the problem statement. In order to calculate the voltage regulation, we need to know the phase angle (Φ2) of the secondary voltage at rated load. Without this information, it is not possible to accurately determine the voltage regulation.

I would suggest reaching out to your lecturer for clarification on the problem statement and to confirm if Φ2 is missing or if it can be calculated from the given data. It is important to have all the necessary information in order to accurately solve the problem.

Thank you and best of luck with your studies.