Motor Calculations part6

Problem-A single-phase motor is taking 20 amperes from a 400- volt, 50-hertz supply, the power factor being 80% lagging. What value of capacitor connected across the circuit will be necessary to raise the power factor to unity?

Solution-With reference to the vector diagram in Fig. 11, it is evident that

The equation for the capacitive reactance is

Inserting values and simplifying

Problem-A 220-volt, 60-hertz, 10-hp, single-phase induction motor operates at an efficiency of 86% and a power factor of 90%. What capacity should be placed in parallel with the motor so that the feeder supplying the motor will operate at unity power factor?

Solution-

The current taken by the motor is

Current taken by the capacitor is

The capacitive reactance of the capacitor is

Capacity necessary is

Problem-In a balanced three-phase, 208-volt circuit, the line current is 100 amperes. The power is measured by the two-wattmeter method; one meter reads 18 k Wand the other zero. What is the power factor of the load? If the power factor were unity and the line current the same, what would each wattmeter read?

Solution-

The expression for power is

Since one wattmeter reads zero, then

With the power factor unity and with the same line current, then

That is, each wattmeter reads 36/2, or 18 kW.

Problem-In a certain manufacturing plant, a single-phase alter nating current of 110 volts, 60 hertz is applied to a parallel circuit having two branches. Branch 1 consumes 27 k W with a lagging power factor of 0.8, while Branch 2 consumes 12 kW with a leading power factor of 0.9. Calculate the

(a) Total power supplied in kW and kVA.

(b) Power factor of the total load.

Solution-

(a) Total power supplied is