Question

You have been hired as new plan manger at a water pumping station. The voltage in the station is 110 V (peak) and frequency 60 Hz. As part of your duty you need to make sure all the electrical motors at the station are compliant with the energy provider requiring to draw current with power factor larger than 0.8(cosϕ>0.8). You notice one of the motors at the station is actually drawing 2 kW of active power with a power factor 0.5 (lagging). At the moment there are only 4 capacitors available to fix the power factor, 2 of them have value of 2500μF and the other two 1000μF.

a) Compute the reactive power absorbed by the motor.

Answer 1

To compute the reactive power absorbed by the motor, use the formula Q = S * sin(ϕ), where S is the apparent power and ϕ is the phase angle. Plug the given values into the equation and solve for Q.

Step-by-step explanation:

To compute the reactive power absorbed by the motor, we can use the formula:

Reactive Power (Q) = Apparent Power (S) * sin(ϕ)

Apparent Power (S) can be calculated as the square root of the sum of the active power (P) squared and the reactive power (Q) squared. In this case, the active power is given as 2 kW (2000 W). So, S = sqrt((P^2) + (Q^2)) = sqrt((2000^2) + (Q^2)).

Since the power factor (cosϕ) is given as 0.5, we can determine sin(ϕ) as sqrt(1 - (cosϕ^2)) = sqrt(1 - (0.5^2)).

Plugging the values into the calculations, we can solve for Q.