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)312 μFc)137.64μFd)105μFCorrect answer is option 'C'. Can you explain this answer?

Question

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&mu;Fb)312 &mu;Fc)137.64&mu;Fd)105&mu;FCorrect answer is option 'C'. Can you explain this answer?

Answer

Calculating Capacitance for Correcting Power Factor:

1. Given Parameters:
- Voltage (V) = 400 V
- Frequency (f) = 50 Hz
- Motor Load (S) = 50 kVA
- Initial Power Factor (p.f.) = 0.75 lagging
- Desired Power Factor = 0.95
- Capacitors are delta connected

2. Calculate Real Power (P):
- Real Power (P) = Apparent Power (S) x Power Factor (p.f.)
- P = 50 kVA x 0.75 = 37.5 kW

3. Calculate Reactive Power (Q) for Initial Power Factor:
- Q = √(S^2 - P^2)
- Q = √((50 kVA)^2 - (37.5 kW)^2)
- Q = 30 kVAr

4. Calculate Reactive Power (Qc) for Corrected Power Factor:
- Qc = P x tan(cos^-1(Desired p.f.))
- Qc = 37.5 kW x tan(cos^-1(0.95))
- Qc = 7.5 kVAr

5. Determine the Capacitive Reactive Power (Qcap) Required:
- Qcap = Q - Qc
- Qcap = 30 kVAr - 7.5 kVAr
- Qcap = 22.5 kVAr

6. Calculate the Capacitance Required:
- For delta connection, each capacitor provides √3 times the rated capacitance
- Qcap = (3 x V^2 x C x 2πf) / √3
- 22.5 kVAr = (3 x (400 V)^2 x C x 2π x 50 Hz) / √3
- C = 137.64 μF

Therefore, the capacitance of each capacitor required to correct the power factor to 0.95 is 137.64 μF.

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