Question

(a) Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of number of turn and currents in the two coils.

(b) A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having 300 turns. Find the number of turns in the secondary to get the power output at 220 V.

Solution

Labelled diagram of a step-down transformer:

Principle:
The transformer is based on the principle of electromagnetic mutual induction.
When the current flowing through the primary coil changes, an emf is induced in the secondary coil due to the change in magnetic flux linked with the primary coil.

ii) Turn ratio in terms of voltage is,
n =

straight N subscript straight s over straight N subscript straight P space equals space V subscript s over V subscript P

iii) For an ideal transformer, according to the law of conservation of energy,
Input electrical power = Output electrical power.
IP VP = IS VS
i.e.,

straight V subscript straight S over straight V subscript straight P space equals space I subscript P over I subscript S

therefore space space space space space straight I subscript straight P over straight I subscript straight s space equals space straight V subscript straight s over straight V subscript straight P equals straight N subscript straight s over straight N subscript straight P rightwards double arrow space space space space straight I subscript straight P over straight I subscript straight s space equals space straight n

iv) Given:
VS = 110 V ; Power,P = 550 W
Power, P = VP IP

rightwards double arrow space straight I subscript straight P space equals space straight P over straight V subscript straight P space equals space 550 over 220 space equals space 2.5 space straight A

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