The Efficiency of an induction motor defined as the ratio between output power and input power.
Induction motor is electrical energy to mechanical energy converter so the input power is nothing but electrical power which is the product of voltage and current but output power is mechanical power which is the product of torque and shaft speed.
The output power of an induction motor is given as
P(output) = ( 2πNT)/ 60.
If we increase the power factor of an induction motor by connecting a capacitor in shunt path then effective VAR increases in the air gap which makes the induced EMF in the rotor bars high as the EMF is directly proportional to the fluxes per pole. As the EMF increases the armature current goes high .
The speed of the rotor rotation is directly proportional to the induced EMF and the electromagnetic torque is directly proportional to the armature current .
Due to this the speed and the electromagnetic torque increases with the aid of effective VAR .
This will increase the product of speed and torque which is nothing but output power