# Unbalanced Three-phase Four-wire, Y-Connected Load

For the three-phase, four-wire, Y-connected load of Fig. 1, conditions are such that none of the load impedances are equal-hence we have an unbalanced polyphase load.
$$\mathbf{V}_{\phi}=\mathbf{E}_{\phi}$$The phase currents can therefore be determined by Ohm's law:$$\mathbf{I}_{\phi_{1}}=\frac{\mathbf{V}_{\phi_{1}}}{\mathbf{Z}_{1}}=\frac{\mathbf{E}_{\phi_{1}}}{\mathbf{Z}_{1}} \text { and so on }$$
The current in the neutral for any unbalanced system can then be found by applying Kirchhoff's current law at the common point $n$:
$$\mathbf{I}_{N}=\mathbf{I}_{\phi_{1}}+\mathbf{I}_{\phi_{2}}+\mathbf{I}_{\phi_{3}}=\mathbf{I}_{L_{1}}+\mathbf{I}_{L_{2}}+\mathbf{I}_{L_{3}}$$