4.a) What is back emf? Derive the relation for the back emf and the supplied voltage in terms of armature resistance(6)
b) The earth-lamps on a main switchboard comprise two 240V 60W lamps connected in the usual manner. The potential difference at the busbars is 220V.Damage by sea water occurs to a distribution cable so that the insulation resistance to the earth is reduced to 16 ohms and 6 ohms for +ve and -ve cables respectively. Find by calculation
(a) which of the two lamps burns the brighter; and
(b) the additional load on the generators occasioned by the fault. The resistance of the cables and the ship's structure may be neglected, and that of the lamps taken as constant at the value corresponding to the 60W rating.(10)
Reference Answer
### Part a) Back EMF and its Relation to Supply Voltage #### 1. Concept of Back EMF Back Electro-Motive Force (EMF), denoted as $$E_b$$, is a voltage that develops in the armature conductors of a DC motor as they rotate and cut through the magnetic field lines of the stator poles. This phenomenon is a direct consequence of Faraday's Law of Electromagnetic Induction. According to Lenz's Law, the direction of this induced EMF is such that it opposes the very cause producing it. In a DC motor, the cause is the supply voltage ($$V$$) driving the armature current ($$I_a$$). Therefore, the Back EMF ($$E_b$$) acts in opposition to the supply voltage.
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