Circuit of a Rotor on an Induction Motor

Here is an equivalent circuit of a rotor on an Induction motor:

Can someone explain How do we arrive at this circuit?

The rotor seems to be only a disc(made of a metal) with conductors embedded near the circumference like here: http://www.ece.umn.edu/users/riaz/animations/imwound.html

• if it's got magnets it isn't an induction motor. Nov 11, 2013 at 18:13
• oops, I meant conductors. Nov 11, 2013 at 18:19
• the equiv circuit you have is not what I was taught. Maybe you can link the source? Nov 11, 2013 at 18:28
• processmodeling.org/theory/electronics/emf/… Nov 11, 2013 at 20:14
• Thanks! that was useful. I came across the circuit online, cant seem to find it. If I come across it again, I will post the link. Nov 11, 2013 at 21:35

There's a pretty good website here. Here's the first picture of the equivalent circuit of the whole motor: -

The section in the OP's question is the secondary side of the picture i.e. the rotor. Resistor $R_R$ represents the real mechanical output power of the motor and $jX_R$ represents the impedance of the rotor winding.

The transformer is there because the rotor is coupled to the stator by transformer action. This diagram is only one-third of the full picture of a 3-phase induction motor.

The website goes through the relatively simple theory of converting the circuit to its more usable form: -

Here, the term "s" is used on the rotor output (represented by $R_2$ now) to properly relate output power to the slip of the rotor compared to synchronous machines that do not slip.

I believe that jXr and Rr are for modeling electrical and magnetic properties of rotor windings (and magnetic circuit). Er is rotor part of theoretical transformer coil (when motor is mechanically stopped stator and rotor windings act like some sort of transformer ).

There are 2 types of rotors:

• cage type, which you described are common. Embedded conductors form secondary "coil". "Windings" are shorted and inaccessible.
• rotor with classic windings. This windings are electrically accessible trough rings on shaft