Total Reactive Power drawn from a three-phase balanced load where line voltage = VL, Line current = IL, Phase voltage = VP and Phase current = lP is given by:

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SSC JE Electrical 05 Jun 2024 Shift 3 Official Paper - 1
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  1. \(\rm \sqrt3 \,V_LI_Lcos\phi \)
  2. \(\rm \sqrt3 \,V_LI_Lsin\phi\)
  3. 3 VPIP cos Φ  
  4. \(\rm \sqrt3 \,V_PI_P sin\phi\)

Answer (Detailed Solution Below)

Option 2 : \(\rm \sqrt3 \,V_LI_Lsin\phi\)
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Detailed Solution

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Formula Use:

  • Active Power (P) = 3VpIp cos ϕ = √3VLIL cos ϕ
  • Reactive Power (Q) = 3VpIp sin ϕ = √3VLIL sin ϕ
     

Where, Vp is phase voltage, Ip is phase current, VL is a line voltage, IL is line current

Solution:

We have,

  • Line voltage = VP,
  • Line current = VL,
  • Phase voltage = VP and,
  • Phase current = lP
     

From the above concept,

Reactive power = √3VLIL sin ϕ

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