A three-phase balanced Y-connected motor draws 6.5 kW when the line voltage is 220 V and the line current is 20 A. Determine the power factor of the motor.

Concept:

Power consumed in a three-phase system is,

\(P = \sqrt 3 {V_L}{I_L}\cos \phi\)

In a star-connected three-phase system,

VL = √3 × Vph

And IL = Iph

In a delta connected three phase system,

VL = Vph

IL = √3 × Iph

Where,

VL is line voltage

Vph is phase voltage

IL is line current

Iph is phase current

Calculation:

Given that,

P = 6.5 kW

V_L = 220 volts

I_L = 20 A

From above concept,

\(P = \sqrt 3 {V_L}{I_L}\cos \phi\)

or, \(cos\phi=\frac{P}{\sqrt3 \times V_L\times I_L}=\frac{6.5\times 1000}{\sqrt3 \times220\times 20}=0.85\)