Question

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

(b) Find the synchronous impedance and reactance of an alternator in which a given field current produces an armature current of 200 A on short circuit and a generated e.m.f. of 50V on open-circuit. The armature resistance is 0.1 ohm. To what induced voltage must the alternator be excited if it is to deliver a load of 100 A at a p.f. of 0.8 lagging, with a terminal voltage of 200 V.

Answer 1

Part (a)

Back electromotive force (back EMF, Eb) is the voltage generated in the armature of a DC motor when it rotates and cuts the magnetic flux. By Fleming's Right-Hand Rule, this induced emf opposes the applied voltage V, as per Lenz's law. Back EMF acts as a self-regulating mechanism that limits the armature current when the motor is running.

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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