A 3 – φ load of 750 kW at 400 V, 50 Hz, operates at

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A 3 – φ load of 750 kW at 400 V, 50 Hz, operates at a power factor of 0.7 lagging. What is the capacitance per phase of a mesh connected capacitor bank to improve the power factor to 0.95 lagging?

1. 3040 µF
2. 2500 µF
3. 3438 µF
4. 2789 µF

Correct Option: C

Power per phase,

P_Ph =	750	= 250 kW
	3

cos φ₁ = 0.7
⇒ φ₁ = 45.57°
∴ tan φ₁ = 1.02
Improved, cos φ₂ = 0.95;
⇒ φ₂ = 18.19°
∴ tan φ₂ = 0.3286
Q_{c_p} = P_P (tan φ₁ – tan φ₂)
= 250 (1.02 – 0.3286)
= 172.83 kVAr/ phase
Now Q_C = V.I_C
Here,

I_C =	V	= V.ωC
	X_C

∴ Q_C = V².ωC

⇒ C =	Q_C
	V².ω