Q$1.$ A small house with a power demand of $100$ kVA and an average power factor of $0\mathrm{.}8$ lagging is fed from a $\backslash (50\backslash$mathrm$\{$~Hz$\},220\backslash$mathrm$\{$~V$\}\backslash )$ single$-$phase source via a $150$ m $-$long two$-$core cable chosen from Table A$6(2)$ attached in clipped direct. Estimate:

a$)$ The rating current and the equivalent impedance of the house.

b$)$ The minimum cable size needed and the equivalent impedance of the cable;

c$)$ The actual current on the cable $($to the machine$)$ when the cable in b$)$ is used;

d$)$ The voltage drops alone the cable and the voltage to the machine.

e$)$ The accrual power consumption in the house.

Draw a circuit and a phasor diagram for the system with the source voltage as reference. State clearly any assumptions made.