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A single phase induction motor draws 12 MW power at 0.6 lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to 0.8 lagging. Assuming that the real and reactive power drawn by the motor remains same as before, the reactive power delivered by the capacitor in MVAR is ____________.
    Correct answer is '7'. Can you explain this answer?
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    A single phase induction motor draws 12 MW power at 0.6 lagging power....
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    A single phase induction motor draws 12 MW power at 0.6 lagging power....
    Explanation:

    Given data:


    • Power drawn by motor, P = 12 MW

    • Initial power factor, pf1 = 0.6 lagging

    • Final power factor, pf2 = 0.8 lagging


    Since the real power drawn by the motor remains the same, the apparent power drawn by the motor also remains the same, i.e.


    • Apparent power drawn by motor, S1 = P / pf1 = 12 MW / 0.6 = 20 MVA

    • Apparent power drawn by motor and capacitor, S2 = S1


    Let the reactive power delivered by the capacitor be Qc.

    The reactive power drawn by the motor before connecting the capacitor can be calculated as:


    • Reactive power drawn by motor before connecting capacitor, Q1 = sqrt(S1^2 - P^2) * sin(arccos(pf1)) = 16 MVAR


    The reactive power drawn by the motor and the reactive power delivered by the capacitor after connecting the capacitor can be calculated as:


    • Reactive power drawn by motor and capacitor, Q2 = sqrt(S2^2 - P^2) * sin(arccos(pf2)) = 9.6 MVAR

    • Reactive power delivered by the capacitor, Qc = Q2 - Q1 = 9.6 MVAR - 16 MVAR = -6.4 MVAR

    • The negative sign indicates that the capacitor is delivering reactive power to the system.

    • Therefore, the reactive power delivered by the capacitor in MVAR is 7 MVAR (absolute value).

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    A single phase induction motor draws 12 MW power at 0.6 lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to 0.8 lagging. Assuming that the real and reactive power drawn by the motor remains same as before, the reactive power delivered by the capacitor in MVAR is ____________.Correct answer is '7'. Can you explain this answer?
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