Q$5.($a$)$ Prove, with clearly stated assumptions, that the generated emf $($E$\_($G$))$ equation of a

DC generator is given by:

E$\_($G$)=($P$($O$)/($N$))/(60)\backslash$times $($Z$)/($A$)$

where P is the number of poles, Z is the total number of conductors in armature, N

is the armature speed in rpm$,\backslash$phi is the flux per pole and A is the number of parallel

paths due to the windings.

$[6$ marks$]$

$($b$)$ Sketch the speed vs armature current characteristics of a shunt, series and

cumulative compound DC motors.

$[5$ marks$]$

$($c$)$ A $4-$pole, $240$ V $,$ wave$-$connected shunt motor gives $10$ kW when running at $1500$

rpm $.$ The motor draws armature and field currents of $40$ A and $1\mathrm{.}0$ A respectively.

It has $540$ conductors and its armature resistance is $0\mathrm{.}15\backslash$Omega $.$ Assume a drop of $1\mathrm{.}3$ V

per brush.

$($i$)$ Draw the equivalent circuit of the motor.

$[5$ marks$]$

$($ii$)$ Calculate the total torque.

$[3$ marks$]$

$($iii$)$ Calculate the motor useful torque and flu$($x$)/($p$)$ole$.$

$[3$ marks$]$

$($iv$)$ Calculate its rotational losses and efficiency.

$[3$ marks$]$