Question

(a) What is back emf? Derive the relation for the back emf and the supplied voltage in terms of armature resistance. (6)

(b) A three-phase induction motor is wound for four poles and is supplied from a 50. Hz system. Calculate: (10)

(i) The synchronous speed;

(ii) The speed of the rotor when the slip is 4 per cent;

(iii) The rotor frequency when the speed of the rotor is 600 r/min.

Answer 1

Part (a)

Consider a shunt motor:

$$V\:=\:Applied\:voltage$$

$$I\:=\:Current\:flowing\:through\:the\:circuit$$

$$R_{a}\:=\:Armature\:resistance$$

$$R_{sh}\:=\:Shunt\:field\:resistance$$

$$I_{sh}\:=\:Shunt\:field\:current$$

$$E_{b}\:=\:Back\:EMF$$

$$Net\:voltage\:across\:Armature\:=\:V-E_{b}$$

$$Current\:=\:\frac{V}{R}$$

$$Therefore,\:I_{a}\:=\:\frac{V-E_{B}}{R_{a}}$$

$$I_{a}R_{a}\:=\:V-E_{b}$$

$$E_{b}\:=\:V-I_{a}R_{a}$$

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