If P is the power of a star connected system, then what will be the power of an equivalent delta connected system?

The correct answer is option 4): 3 P

Concept:

Let the star-connected system is denoted as (Y)

V_L is the line voltage

V_ph is the phase voltage

I_L is the line current

I_ph is the phase current

V_ph = \(V_L\over \sqrt(3)\)

I_L = I_Ph = \(V_{ph}\over R\)

Power = 3 × I_ph² × R

P_Y = \(V_L^2 \over R\)

For delta connection ( Δ )

I_L = \( I_{Ph} \over \sqrt{3}\) = \(V_{ph} \over R\)

P_Δ  = 3 × Iph2 × R

= 3 × (\(V_{ph} \over R\))² × R

PΔ =  3 × \(V_L^2 \over R\)

PΔ  =  3 × PY

Hence option 4 is correct