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GATE 2014 EC (EC1) – Question 41

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 2 marks · Multiple choice

A 230 V rms source feeds two parallel loads: 10 kW at 0.8 leading power factor, and 10 kVA at 0.8 lagging power factor. Find complex power delivered by the source.

  1. (18 + j1.5) kVA
  2. (18 − j1.5) kVA
  3. (20 + j1.5) kVA
  4. (20 − j1.5) kVA

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Correct answer: (B) (18 − j1.5) kVA

Explanation

The first load has P1=10kW and leading power factor0.8, so Q1=−P1tan(arccos0.8)=−7.5kVAr. The second has apparent power10kVA at lagging0.8, giving P2=8kW and Q2=6kVAr. Add complex powers: S=18−j1.5kVA, **B**. Leading reactive power is negative.