Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

An industrial load with an operating voltage of 480/0° V is connected to the power system. The load absorbs 120 kW with a lagging power factor of 0.77. Determine the size of the capacitor in vars that is necessary to raise the power factor to 0.9 lagging.

Sagot :

okpalawalter8

Answer:

[tex]Q=41.33 KVAR\ \\at\\\ 480 Vrms[/tex]

Explanation:

From the question we are told that:

Voltage [tex]V=480/0 \textdegree V[/tex]

Power [tex]P=120kW[/tex]

Initial Power factor [tex]p.f_1=0.77 lagging[/tex]

Final Power factor [tex]p.f_2=0.9 lagging[/tex]

Generally the equation for Reactive Power is mathematically given by

Q=P(tan \theta_2-tan \theta_1)

Since

[tex]p.f_1=0.77[/tex]

[tex]cos \theta_1 =0.77[/tex]

[tex]\theta_1=cos^{-1}0.77[/tex]

[tex]\theta_1=39.65 \textdegree[/tex]

And

[tex]p.f_2=0.9[/tex]

[tex]cos \theta_2 =0.9[/tex]

[tex]\theta_2=cos^{-1}0.9[/tex]

[tex]\theta_2=25.84 \textdegree[/tex]

Therefore

[tex]Q=P(tan 25.84 \textdegree-tan 39.65 \textdegree)[/tex]

[tex]Q=120*10^3(tan 25.84 \textdegree-tan 39.65 \textdegree)[/tex]

[tex]Q=-41.33VAR[/tex]

Therefore

The size of the capacitor in vars that is necessary to raise the power factor to 0.9 lagging is

[tex]Q=41.33 KVAR\ \\at\\\ 480 Vrms[/tex]

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.