3. (4pts) A three-phase transformer has electrical parameters $r_1 = r_2 = 5\Omega$, $X_{e1} = X_2 = 5\Omega$, and $X_m = 100\Omega$. The primary side of the transformer is connected to a 480 V (line-line), 60 Hz utility voltage source. The secondary side is connected to a Y-connected load with phase impedance (referred to the primary winding) of $Z_p = 3.75 + j1.25\Omega$.
a) (3pts) Determine the $a$-phase current, the real and reactive power supplied by the voltage source, and the power factor seen by the source.
b) (1pt) Assume that magnetizing impedance is very large ($X_m \to \infty$) and recalculate the $a$-phase current. What is the error in the magnitude of the current (compared to part a) using this assumption?