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Question

Draw a labeled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of the number of turns and current in the two coils.


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Solution

Definition of a step-up transformer:

  1. A transformer is an electrical device that transforms the electrical energy (in the primary coil) into magnetic energy (in the magnetic coil) and then back again into electrical energy (in the secondary coil).
  2. A step-up transformer is a device that converts a low voltage high current into a high voltage low current.
  3. The transformer works on the principle of faradays law which is V=-dϕdt.
  4. The ac current is passed through the primary coil which produces a change in the magnetic field of the magnetic core which in turn produces a current in the secondary coil.

Given below is a labelled diagram of the step-up transformer,

Calculation of the ratio of secondary to primary voltage in terms of the number of turns and current in the two coils:

Step 1: Given

Let the alternating voltage, alternating current, and the number of turns in the primary and secondary coil be V1,I1,N1and V2,I2,N2.

Magnetic flux in a coil is proportional to the number of turns.

Therefore ϕsecϕpri=N2N1

Here,

ϕ indicates flux in a coil.

Step 2: Calculation

ϕsec=N2N1ϕpri

dϕsecdt=N2N1dϕpridt

But according to faradays law V=-dϕdt

Therefore V2V1=N2N1

Let us assume a 100 percent efficiency.

This implies input power= output power

V1I1=V2I2

Hence, the ratio of secondary to primary voltage will be V2V1=N2N1=I1I2.


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