Q$4.$ An unbalanced three phase load is supplied from a $440V,50Hz$ four wire supply. The current in the Brown line is $6$ A $,$ lagging by $30,$ the current in the Black line is $5$ A in phase and the current in the Grey line is $7$ A $,$ leading by $15.$

Determine EACH of the following:

$($a$)$ the current in the neutral line; $(10$ marks$)$

$($b$)$ the total power dissipated by the circuit. $(5$ marks$)$

$($c$)$ Sketch the phasor diagram of Load and Neutral currents.

$(5$ marks$)$