Transformers

An electrical device which converts low alternating voltage at high current to high alternating voltage at low current (or vice versa) — i.e., a device which reduces or increases the voltage in an AC circuit through mutual induction — is called a transformer.

 P_input = P_output

A transformer is based on the principle of mutual induction, i.e., whenever the magnetic flux linked with a coil changes, an emf is induced in the neighbouring coil. For an ideal transformer there is no loss of power, so P_input = P_output​. On the basis of winding, transformers are of two types — step-up and step-down.

A transformer consists of three main components:

Laminated Soft Iron Core

• Provides a closed magnetic path for the flux
• Made of thin silicon-steel laminations (insulated from each other)
• Laminations reduce eddy current losses
• Soft iron is used because it has low hysteresis loss and high permeability

Primary Coil (Winding)

• Input coil connected to the AC source
• Has Nₚ turns of insulated copper wire
• Draws alternating current from the source

Secondary Coil (Winding)

• Output coil connected to the load
• Has Nₛ turns of insulated copper wire
• Delivers the transformed voltage/current to the circuit

1. Alternating voltage Vₚ is applied across the primary coil (Nₚ turns).
2. An alternating current Iₚ flows, generating a time-varying magnetic flux Φ in the soft iron core.
3. This changing flux threads through both coils (assuming no flux leakage).
4. By Faraday's Law, an EMF is induced in both coils:
   In primary: eₚ = −Nₚ (dΦ/dt)
   In secondary: eₛ = −Nₛ (dΦ/dt)
5. The secondary EMF drives current through the connected load, delivering AC output.

\[\frac{V_s}{V_p}=\frac{N_s}{N_p}=k\]

Where:

• V_s = Secondary (output) voltage (V)
• V_p = Primary (input) voltage (V)
• N_s = Number of turns in secondary coil
• N_p = Number of turns in primary coil
• k = Transformation ratio (turns ratio)

\[\frac{I_p}{I_s}=\frac{N_s}{N_p}=\frac{V_s}{V_p}\]

\[\frac{V_s}{V_p}=\frac{N_s}{N_p}=\frac{I_p}{I_s}=k\]