Introduction

Transformers are essential electromagnetic devices that transfer electrical energy between circuits through electromagnetic induction. They play a crucial role in power distribution and electronic devices by converting voltage levels while maintaining power.

Core Principles of Transformer Operation

Transformers work based on Faraday's law of electromagnetic induction. When an alternating current (AC) flows through the primary coil, it generates a time-varying magnetic field. This changing magnetic field induces a voltage in the secondary coil through electromagnetic induction.

The Role of the Iron Core

The transformer's soft iron core serves two critical functions:

The high magnetic permeability of iron (typically 5000 times that of air) ensures efficient magnetic flux transfer between coils.

Mathematical Analysis of Ideal Transformers

An ideal transformer operates with 100% efficiency and perfect coupling between coils. Two fundamental equations govern its operation:

Voltage Ratio Equation

The relationship between primary and secondary voltages is given by:

$\frac{V_p}{V_s} = \frac{N_p}{N_s}$

Where:

Power Conservation Equation

In an ideal transformer, input power equals output power:

$V_p I_p = V_s I_s$

Where:

Combining these equations gives us:

$\frac{N_p}{N_s} = \frac{V_p}{V_s} = \frac{I_s}{I_p}$

Lenz's Law and Phase Relationships

Lenz's law manifests in transformers through the phase relationship between primary and secondary currents. The induced current in the secondary coil generates a magnetic field that opposes the change in magnetic flux that created it. This results in:

AC vs DC Operation

Transformers only operate effectively with AC power because:

While pulsed DC can theoretically operate a transformer, it's impractical for real-world applications due to: