$($a$)$

The nameplate on a $350$ V$,60$ Hz$,4$ pole induction motor indicates its rated speed at rated load is $1752$ rpm$.$ When operating at rated load, determine

$($i$)$

the angular velocity of the stator produced air gap wave with respect to the stator and

$($ii$)$

the angular velocity of the rotor produced air gap wave with respect to the stator and with respect to the rotor?

$[1]$

$[3]$

$($b$)$

A $3$ phase, $415$ V$,50$ Hz$,8$ pole, squirrel cage induction motor is running at $725$ rpm$.$ The power input at this speed is $35$ kW$.$ Stator losses are $0\mathrm{.}65$ kW and the friction and windage losses are $0\mathrm{.}4$ kW$.$

$($i$)$

When do the following value of slip occur

$$

s $=0$

$$

s $=1$

$$

s $<0$

$($ii$)$

Calculate the slip and the power delivered to the rotor, Pgap.

$($iii$)$

Calculate the mechanical power developed and hence determine the rotor losses.

$($iv$)$

Calculate the efficiency of the machine.

$[3]$

$[3]$

$[2]$

$[1]$

$($c$)$

A $4$ pole, $50$ Hz$,1500$ V$,$ class B induction machine is rated at $32$ kW$.$ It has a full load speed of $1460$ rpm and stator resistance of $2\mathrm{.}8/$phase$.$

$($i$)$

If the rotor resistance is increased, describe with brief explanation what happens to :

$$

the value of maximum torque,

$$

the slip, and

$$

the startup torque if the rotor resistance is increased.

$($ii$)$

Calculate the full load torque for the machine.

$($iii$)$

Using standard notation for blocked rotor tests, calculate the value of XBR$,$ if the results of a blocked rotor test are given as:

f $=12\mathrm{.}5$ Hz$,$ VLL $=415$ V$,$ IL $=18$ A$,$ Input Power $=8700$ W$.$

Calculate the value of XBR$.$