# Torque, Current and Voltage Relationship in Induction Motor

In induction motor, Torque is proportional to square of applied stator voltage (I agree that) but some source says torque is proportional to current. For me something proportional to square of volt should be proportinal to square of current as well. Is that right?

This source may be meaning under constant voltage torque is proportional to current? May it be?

• Perhaps providing a link to the source you're talking about would generate better answers. – Scott Seidman Jun 6 '19 at 13:01
• discussing an induction motor without including slip explcitly is rather dooooomed from the start. – Neil_UK Jun 6 '19 at 13:07
• Better: The torque drops with inverted voltage square, current is proportional to the output torque (at certain region) – Marko Buršič Jun 6 '19 at 13:08
• First, I believe you mean "some sources" -- "some source" to a native English speaker means "exactly one source and I'm not going to tell you who". Second, whether it is a singleton or multiple sources, give us citations -- a web link, or a proper bibliographic citation if it's a book or magazine article. If it's a number of sources, pick one or two that you think is most representative. – TimWescott Jun 6 '19 at 16:14

In induction motor, Torque is proportional to square of applied stator voltage

Very likely true when the rotor is locked, mostly true when slip is a good fraction of 1, and pretty much utterly false when the motor is running close to its synchronous speed. By their nature, induction motors have zero torque exactly at their synchronous speed, no matter how much power they may be burning up for other reasons.

but some source says torque is proportional to current.

Are you sure that this unnamed source is talking about induction motors? For a 100% efficient motor the output power will equal the input power; at a fairly constant speed, a fairly efficient motor will have an input power roughly equal to the output power -- if you assume constant excitation voltage this would translate to a torque that's proportional to the proportion of current that's in phase with the voltage.

For me something proportional to square of volt should be proportinal to square of current as well. Is that right?

That is correct if the "something" is governed by Ohm's law. Only resistors are strictly subject to Ohm's law.

This source may be meaning under constant voltage torque is proportional to current?

Yes. The source must be saying that and a bit more.

The torque capability of an induction motor is proportional to the square of voltage over some range above and below the rated voltage.

The operating torque of a motor is the torque where the torque capability curve of the motor intersects the torque demand or requirement curve of the load. Assuming that the motor is operating below or only a little above its rated torque for continuous operation, the current at the steady-state operating point is proportional to torque.

• @EuanM: Thank you. I corrected that. – Charles Cowie Nov 24 '19 at 11:55
• I've deleted my comment :-) I'm assuming that it's the torque that varies with current supplied, rather than vice versa? – Euan M Nov 25 '19 at 22:33
• @EuanM: With the usual methods of operating induction motors, the voltage and frequency are "supplied." The motor's speed, torque, current and power factor depend on the motor's characteristics and the characteristics of the driven load. The current is not "supplied." The load torque determines the current drawn from the source by the motor. – Charles Cowie Nov 25 '19 at 23:30