A slipring motor has it's rotor terminals available to the outside world through sliprings. The rotor resistance can be varied by connecting external resistance through sliprings. This method is particularly useful when we want to change the starting torque or change the speed for which maximum torque can take place.
A squirrel cage motor has its rotor windings completely isolated from the external world. To be more precise, a squireel cage rotor has iron bars as conductors shorted by end rings. There are no copper wire windings. Because of this this motor is rugged.
It goes a little deeper than that, only in that "slip ring motor" is not technically a valid definition of a motor type (although incorrectly used that way by many). it is a technology description for making the rotor connections only. Some "slip ring motors" are technically called Wound Rotor Induction Motors (WRIM) as described above, but if you used the "slip ring" in an acronym, it would be SRIM, which already means Switched Reluctance Induction Motor. AC Synchronous Motors are also mistakenly referred to as "slip ring motors" by others, so you have to be more specific to avoid confusion, although technically a Synchronous Motor s not considered an induction motor (as per the original subject line). I know I am being a bit pedantic, but the misuse of "slip ring motor" a pet peeve of mine.
In a Synchronous motor, the slip rings are used to supply DC to the windings in the rotor, which controls the field strength and thus alters the reactive power.
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