A 220 V, 8 kW, 50 Hz, 1 – φ motor working at full

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A 220 V, 8 kW, 50 Hz, 1 – φ motor working at full load with an efficiency of 85% has a power factor of 0.8 lagging. If a capacitor is connected across the motor terminals to raise the overall power factor to unity, then current through the capacitor will be

1. 33.5 amps
2. 32.0 amps
3. 30 amps
4. 41 amps

Correct Option: B

Power input, P =	8000	= 9.411 kW
	0.85

Q_C = P (tan φ₁ – tan φ₂)
Now cos φ₁ = 0.8
⇒ φ₁ = 36.86°
∴ tan φ₁ = 0.749
and cos φ₂ = 1,
⇒ φ₂ = 0°
∴ tan φ₂ = 0
∴ Q_C = 9.411 (0.749 – 0) = 7.048 kVAr.
Now Q_C = V.I_C

⇒ I_C =	Q_C	=	7.048 × 10³
	V		220

= 32.03 amp.