A three-phase generator delivers voltages V A (t) = V 0 cost, V B (t) = V

Question:

A three-phase generator delivers voltages V_A(t) = V₀ cosωt, V_B(t) = V₀ cos(ωt + 2π/3), and V_C(t) = V₀ cos (ωt − 2π/3). First, assume that all three phases are connected to identical, purely resistive loads. Show that the total power delivered is 3V²₀ /2R, independent of time. Next, assume that the loads have impedance|Z|eⁱ^φ, and show that the total power remains time independent. What is the role of the power factor,cos φ?