Question $1[15$ marks$]$A $250$ V$,1700$ rpm shunt dc motor operating at rated conditions driving a constant torque$-$load, has a line current of $41\mathrm{.}6$ A when fed by rated terminal voltage of $250$ V$.$ Thearmature resistance and field resistance are: $0\mathrm{.}4$ ohms and $250$ ohms respectively.If the rotational losses of the motor are negligible, calculate the following:

a$)$ armature current;

b$)$ output power;

c$)$ mechanical developed torque;

d$)$ efficiency.

Now, assume that we reduce the field resistance to $200$ ohms. Under these newconditions $($assuming a linear magnetic circuit$)$ calculate:

a$)$ new armature current;

b$)$ new line current;

c$)$ new motor speed

d$)$ output power.

Question $2[5$ marks$]$A DC shunt motor, rated at $20$ HP$,230$ V$,1250$ rpm has an armature resistance of $0\mathrm{.}18$Ohms. At rated speed and load, the armature current is $78$ A$,$ and the field current is $1\mathrm{.}8$A$.$Determine:

a$.$ Ea$,$ the induced armature voltage;

b$.$ The output torque;

c$.$ The mechanical losses;

d$.$ The efficiency.

Question $3[15$ marks$]$A three$-$phase, $480$ V$,60$ Hz$,100$ HP$,$ Y$-$connected, $6-$pole wound rotor induction motorhas the following parameters in ohm$/$phase referred to the stator,

R$1=0\mathrm{.}1$X ohm $.,=.,=.,=.,=.$ Rotational losses are assumed to be constant and evaluated to be $2950$ W$.$ If the motoris operating at a slip of $3\mathrm{.}3\%$ at rated voltage and frequency, determine:

a$.$ The line current;

b$.$ The stator copper loss;

c$.$ The air$-$gap power;

d$.$ The rotor copper loss;

e$.$ The mechanical developed power

;f$.$ The mechanical developed torque

;g$.$ The shaft torque

;h$.$ The efficiency.

Question $4[15$ marks$]$A $4-$ploe, $230$ V$,3-$phase, $60$ Hz$,$ Y$-$connected SCIM has the following equivalentparameters on a per$-$phase basis:

R$1=0\mathrm{.}1$ ohm X $1=0\mathrm{.}205$ ohm,

R$2=0\mathrm{.}079$ ohm X$2=0\mathrm{.}186$ohm

Xm$=7\mathrm{.}5$ ohm

Mechanical losses are $5\mathrm{.}9$ W$,$ and core losses are $10\mathrm{.}72$ W$.$ If the motor operated at itsrated speed of $1550$ W$,$ find the following:

a$.$ The stator current

;b$.$ The magnetization current;

c$.$ The rotor current;

d$.$ The power input;

e$.$ The stator copper losses

;f$.$ The rotor copper losses;

g$.$ The power output

;h$.$ The shaft torque

;i$.$ The motor efficiency