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The Balanced ThreePhase DeltaConnected LoadAuthor: E.E. Kimberly If a group of three identical resistances R_{12}, R_{23} and R_{31} or three identical impedances Z_{12}, Z_{23}, and Z_{31} are connected in delta, as in Fig. 93 (a) or Fig. 93 (b), and are then connected to a source of threephase voltages, three equal currents will flow in the three phase or branch impedances. If the three linetoline voltages have the phase sequence V_{31}, V_{23}, and V_{12}, they will produce currents I_{31}, I_{23}, and I_{12}, respectively, in the three impedances. If the impedances are purely resistive, the currents are in phase with the voltage drops across the respective impedances, as in (c). The angle θ in (d) between any current and the voltage which produces it will be the characteristic angle of the impedance through which the current flows.
At a corner of the voltage delta, such as 3, I_{23} is positive to the corner and I_{31} is negative to the corner. The corner 3 of the voltage delta corresponds to line 3 on the associated circuit diagram. The line current at terminal 3 is made up of the currents of the two phase branches connected to it. Therefore, I_{3} = I_{23} + ( I_{31}) or I_{23}I_{31}. Inasmuch as the phases have been assumed to be of identical impedances, the angle between I_{23} and I_{31} is 60°. Therefore, I_{3} = 1.732*I_{23} or


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