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It is desired to correct the p.f. to 0.95 by means of static capacitors connected across each phase of a 3-phase, 400 V, 50 Hz motor having a maximum load of 50 kVA at a p.f. of 0.75 lagging. The capacitors are delta connected. What is the capacitance of each capacitor?
- a)174 μF
- b)312 μF
- c)137.64 μF
- d)105 μF
Correct answer is option 'C'. Can you explain this answer?
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It is desired to correct the p.f. to 0.95 by means of static capacitor...
Capacitive current/phase,
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It is desired to correct the p.f. to 0.95 by means of static capacitor...
ΜF
b)261 µF
c)348 µF
d)435 µF
We can first calculate the reactive power of the motor:
Q = S * sqrt(1 - pf^2) = 50,000 * sqrt(1 - 0.75^2) = 30,000 VAR
To correct the power factor to 0.95 lagging, we need to add capacitive reactive power:
Qc = S * (1/pf - 1/pf') * sqrt(pf'^2 - 1) = 50,000 * (1/0.75 - 1/0.95) * sqrt(0.95^2 - 1) = 17,320 VAR
Since the capacitors are delta connected, the line voltage across each capacitor is 400 V, and the reactive power per capacitor is:
Qc_cap = Qc/3 = 5,773 VAR
The capacitance can be calculated from the reactive power and the voltage:
Qc_cap = (2*pi*f*C*V^2)/3
C = Qc_cap/(2*pi*f*V^2/3) = 348 µF (approx.)
Therefore, the answer is (c) 348 µF.
b)261 µF
c)348 µF
d)435 µF
We can first calculate the reactive power of the motor:
Q = S * sqrt(1 - pf^2) = 50,000 * sqrt(1 - 0.75^2) = 30,000 VAR
To correct the power factor to 0.95 lagging, we need to add capacitive reactive power:
Qc = S * (1/pf - 1/pf') * sqrt(pf'^2 - 1) = 50,000 * (1/0.75 - 1/0.95) * sqrt(0.95^2 - 1) = 17,320 VAR
Since the capacitors are delta connected, the line voltage across each capacitor is 400 V, and the reactive power per capacitor is:
Qc_cap = Qc/3 = 5,773 VAR
The capacitance can be calculated from the reactive power and the voltage:
Qc_cap = (2*pi*f*C*V^2)/3
C = Qc_cap/(2*pi*f*V^2/3) = 348 µF (approx.)
Therefore, the answer is (c) 348 µF.
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It is desired to correct the p.f. to 0.95 by means of static capacitors connected across each phase of a 3-phase, 400 V, 50 Hz motor having a maximum load of 50 kVA at a p.f. of 0.75 lagging. The capacitors are delta connected. What is the capacitance of each capacitor?a)174μFb)312μFc)137.64μFd)105μFCorrect answer is option 'C'. Can you explain this answer?
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