Star connection:

• The three phase windings have one end of each connected to a common neutral point; the other ends form the three line terminals.
• Line current = phase current: IL = Iph (the same current flows through the winding and the line).
• Line voltage = root 3 x phase voltage: VL = root 3 x Vph. The line voltage is the phasor difference of two phase voltages, which are 120 degrees apart, giving a magnitude of root 3 times the phase voltage.
• Vector diagram: three phase voltages VRN, VYN, VBN at 120 degrees; the line voltage VRY is the phasor sum of VRN and (-VYN), equal to root 3 Vph and leading the phase voltage by 30 degrees.

Delta connection:

• The three windings are connected end to end to form a closed loop, the junctions forming the three line terminals.
• Line voltage = phase voltage: VL = Vph (each winding is directly across two lines).
• Line current = root 3 x phase current: IL = root 3 x Iph. The line current is the phasor difference of two phase currents, giving root 3 times the phase current.
• Vector diagram: three phase currents at 120 degrees; the line current is root 3 times the phase current and lags the phase current by 30 degrees.
• Power in both cases: P = root 3 x VL x IL x cos phi.

• |Z| = sqrt(8^2 + 12^2) = sqrt(64 + 144) = sqrt(208) = 14.42 ohm.
• cos phi = R/|Z| = 8/14.42 = 0.555.

(i) Phase current: in delta, phase voltage = line voltage = 415 V. Iph = Vph/|Z| = 415/14.42 = 28.78 A.

(ii) Line current: IL = root 3 x Iph = 1.732 x 28.78 = 49.85 A.

(iii) Power consumed by each phase: Pph = Iph^2 x R = 28.78^2 x 8 = 828.3 x 8 = 6626 W (6.63 kW).

• Total power = 3 x 6626 = 19.88 kW (also = root 3 x 415 x 49.85 x 0.555 = 19.88 kW).