# AC single phase induction motor - phase difference problem

I want to build and AC single phase induction motor. There's the following schematic for its construction.

This motor can only work if there's a 90º phase difference between $I_1$ and $I_2$ as you can see written here, on the Construction section. I did some circuit analysis and I found the following relation:

$$\bar{I}_2=\frac{w L_1}{wL_2-\frac{1}{wC}}\bar{I}_1$$

So, according to this relation, there only can be a 0 or 180º phase difference between the two currents. Did I do something wrong?

• Windings have resistance as well as inductance. (Also, the phase difference does not have to be 90 degrees : that's the ideal condition, but the motor will start as long as the start winding's phase has a substantial 90 degree component)
– user16324
Commented Mar 4, 2016 at 12:30
• Most of the current in the main winding is in phase with the applied voltage, because power is needed to drive the load; VAR can't drive anything
– Chu
Commented Mar 4, 2016 at 13:42