Since the phase impedances of a balanced star- or delta-connected load contain equal currents, the phase power is one-third of the total power. As a definition, the voltage across the load impedance and the current in the impedance can be used to compute the power per phase.
Let's assume that the angle between the phase voltage and the phase current is θ, which is equal to the angle of the impedance. Considering the load configurations given in below fig, the phase power and the total power can be estimated easily.
In case of delta conneted load in above fig(a) the total active power is equal to three times the power of one phase.
substituting this eq the total active power becomes
substituting this in Ptotal we wil get the same equation as that for the delta connected load.
Similarly, the total reactive and the total apparent power in the three-phase balanced ac circuits can be given by
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