The equation for active power in a three-phase star connected circuit is:

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SSC JE Electrical 15 Nov 2022 Shift 2 Official Paper
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  1. P = \(\sqrt{3}\)VL IL sin ϕ 
  2. P = 3VL IL sin ϕ 
  3. P = 3VL IL cos ϕ 
  4. P = \(\sqrt{3}\)VL IL cos ϕ 

Answer (Detailed Solution Below)

Option 4 : P = \(\sqrt{3}\)VL IL cos ϕ 
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Detailed Solution

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Power in 3ϕ circuit:

Case 1: In star connection

The active power is given by:

\(P=\sqrt{3}V_LI_L\space cos\phi\)

The reactive power is given by:

\(Q=\sqrt{3}V_LI_L\space sin\phi\)

The apparent power is given by:

\(S=\sqrt{P^2+Q^2}\)

\(S=\sqrt{3}V_LI_L\)

Case 2: In delta connection

The active power is given by:

\(P={3}V_PI_P\space cos\phi\)

The reactive power is given by:

\(Q={3}V_PI_P\space sin\phi\)

The apparent power is given by:

\(S=\sqrt{P^2+Q^2}\)

\(S=3V_PI_P\)

Here, VL and Iare line voltage and line current

Vp and Ip are phase voltage and phase current

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