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VinnyCee
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Homework Statement
A three phase, 6-pole, [itex]\Delta[/itex] connected induction motor is rated 208V, 60Hz. It has [itex]R_R\,=\,5.2\,\Omega[/itex], [itex]R_S\,=\,2.2\,\Omega[/itex], [itex]X_m\,=\,220\,\Omega[/itex], [itex]X_{lr}\,=\,7.5\,\Omega[/itex], [itex]X_{ls}\,=\,2.3\,\Omega[/itex].
Calculate the starting torque and both phase and line currents when the motor is started in [itex]\Delta[/itex] and Y.
Homework Equations
Various equations from the notes about induction machines and multiple pole pairs.
[tex]I_{S,\,Y}\,=\,\frac{\frac{V_{rated}}{\sqrt{3}}}{(R_S\,+\,j\,X_{ls})+(j\,X_m\,||\,R_R\,+\,j\,X_{lr})}[/tex]
[tex]T_Y\,=\,3\,\cdot\,\frac{P_{gap}}{\omega_s}\,\cdot\,\frac{p}{2}[/tex]
[tex]I_{R,\,Y}\,=\,I_{S,\,Y}\,\cdot\,\frac{j\,X_m}{R_R\,+\,j\,X_{lr}\,+\,j\,X_m}[/tex]
[tex]P_{gap}\,=\,|I_{R,\,Y}|\,\cdot\,R_R[/tex]
The Attempt at a Solution
[tex]I_{S,\,Y}\,=\,\frac{\frac{208}{\sqrt{3}}}{(2.2\,+\,j\,2.3)+(j\,220\,||\,5.2\,+\,j\,7.5)}\,=\,10\,\angle\,-53.8^{\circ}[/tex]
In Y, the line current is same as phase current above, right?
I get the torque in Y as [itex]T_Y\,=\,11.68\,Nm[/itex].
Does that look right?
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