Single Phase Induction motor winding phase difference

[Vikas Kasireddy]

Q1:
So I'm trying to extract the electrical properties of a single phase induction motor. First off, how am I supposed to measure the phase difference between the start and run windings? I have L and R of start and run windings too!
Q2:
I have a torque vs slip curve up until 130% of rated load. Using this I was told I'm supposed to curve fit this data to the equation Torque*c1 = c2*s/(1+(j*w*t)) to get the time constant t of the rotor (or L/R of the rotor). I'm not sure how I'm supposed to do this. I also have this L/R value using the electrical model that I found with locked rotor measurements.
Q3:
If this system was to be switched with a capacitor to get 90 degrees phase shift, how do I calculate the capacitor value? I know I'm supposed to draw a phasor diagram and find the value of C so that it forms the required phase shift but I need more explication on that.

 

[scottdave]

For the phasor diagram. You should have a phasor pointing somewhere in quadrant I (up and to the right). Up is for the inductive portion, and horizontal is resistive portion. If you create a right triangle from this coming back down to the Real axis, this vertical leg coming down will be your capacitive phasor.

Do you know how to calculate capacitive reactance from Capacitance and Frequency?