A $400$ V three phase Main Switchboard $($MSB$)$ as shown in Figure Q$4$ supplies to a three phase $150$ kW electric motor with power factor of $0\mathrm{.}85$ lagging and efficiency of $90\%$ which is located $80$ metres away.

The electric circuit from the MSB to the motor is laid horizontally, touching on a cable tray using single$-$core, copper conductor, XLPE insulation and PVC sheath cables.

The section of the electric circuit from the MSB in the corridor is $25$ metres long. It shares with another two circuits and the ambient temperature is $35\backslash$deg C$.$The section of the electric circuit in the furnace room to the motor is $55$ metres long and is on its own. The ambient temperature in the furnace room is $50\backslash$deg C$.$ Overload protection of the cables is by a Triple Pole $($TP$)$ MCCB in the MSB$.$ Earth fault protection is by an Earth Leakage Relay with current setting of $2$ A and time setting of $0\mathrm{.}3$sec$.$

$($a$)$ Select the appropriate cable size for the cable to the motor. The cable is required to be protected against overload.$(6$ marks$)$

$($b$)$ Calculate the voltage drop in the steady load conditions when the motor is operating at full load.

$($c$)$ During motor starting, the power factor drops to $0\mathrm{.}3$ and the starting current is $3$ times or starting, th eurrent, calculate the voltage drop during motor starting.$(3$ marks$)$

$($d$)$ The earth fault loop impedance measured at the motor is $0\mathrm{.}6$ S$,$ what is the prospective earth fault current?$(2$ marks$)$

$($e$)$ A single core, copper, PVC insulated cable is used as the circuit protective conductor of the motor, use the Table $5\mathrm{.}5$ below to determine the cable size of the circuit protective conductor.$(2$ marks$)$

$($f$)$ Check whether the circuit protective conductor size is adequate to withstand the thermal effect of the earth fault current.