Handbook of Electrical Engineering

INDUCTION MOTORS 103

Figure 5.3 Approximate deep-bar resistance reactance curves for four-pole motors rated from 10 kW to
10 MW.

The torqueTe developed in the rotor shaft can be expressed as a function of the air-gap
voltageVm:-

Te=

sR 2 Vm^2

R 22 +(sX 2 )^2

Newton metres

WhereR 2 andX 2 are both functions of the slipsas explained above. The air-gap voltage can be
found from the supply voltageVsby noting that a voltage divider circuit exists which consists of the
series components of the stator and the parallel combination of the magnetising branch and the rotor
circuit. HenceVmbecomes:-

Vm=

VsZ 2 m

Z 1 +Z 2 m

where
Z 1 =R 1 +jX 1

and

Z 2 m=

1

1

Rc

+

1

jXm

+

1

R 2 +Rout+jX 2

but

R 2 +Rout=

R 2

s

and

Rout=

R 2 ( 1 −s)

s