## Transformers

Often we have given voltage which we need to change into some other voltage for a given purpose. The voltage is transformed using a transformer. Transformers work only with alternating current, using the principle that a changing current induces a magnetic field, and that a changing magnetic field induces a current with the ratio between primary or input voltage or current and secondary or output voltage or current being given by the turns ratio:

A step up transformer increases the voltage and decreases the current, while a step down transformer decreases the voltage and increases the current. The alternating voltage in the primary coil creates an alternating magnetic field in the transformer coil. The alternating magnetic field passes around the core, through the secondary coil and induces a changing voltage in the secondary coil. The value of the induced voltage is proportional to the rate of change of flux linkage, which increases with the number of turns in the secondary coil, so that primary and secondary voltages are related by the turns ratio.

All values ofandcan be calculated using the following steps given the input voltage

The output voltage is calculated by rearrangingto give

The current in the secondary coil can be found using

The load, connected to the secondary coil requires a certain current at the secondary voltage. We can useto find this power.

Assuming the transformer to be ideal, the power supplied to the load equals the power supplied to the primary coil.

The primary current can be found by rearrangingto give