A 3 – φ induction motor takes 100 kW at 415 V, 50

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A 3 – φ induction motor takes 100 kW at 415 V, 50 Hz and a power factor of 0.80 lagging. What is the kVAr rating of a capacitor bank to improved the power factor to 0.9 lagging, if the capacitor bank is connected to delta ?

1. 6.25
2. 7.99
3. 7.91
4. 8.82

Correct Option: D

Power per phase =	100	= 33.33 kW
	3

Power factore, cos φ₁ = 0.8
⇒ φ₁ = 36.85°
∴ tan φ₁ = 0.749
Final power factor,
cos φ₂ = 0.9
⇒ φ₂ = 25.84°
∴ tan φ₂ = 0.4843
Reactive power, Q_{c_p} = P_P (tan φ₁ – tan φ₂)

=	100	(0.749 – 0.4843)
	3

= 8.82 kVAr/phase