Transformers

A transformer works on the principle of electromagnetic induction and Faraday's law of induction. The voltage induced in the secondary coil is proportional to the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. This relationship is given by the equation: Where and are the voltages in the secondary and primary coils, and and are the number of turns in the secondary and primary coils.
In a step-up transformer, the number of turns in the secondary coil is greater than the primary coil, which increases the voltage. In a step-down transformer, the number of turns in the secondary coil is less than the primary coil, which decreases the voltage.
Given that , the ratio of turns is , and the resistance in the secondary coil is , we can calculate the current flowing in the secondary coil using Ohm's law: Since the transformer is ideal, the voltage ratio is equal to the turns ratio: Now, calculate the current in the secondary: By conservation of energy and assuming an ideal transformer, the current in the primary coil is related to the current in the secondary by the inverse of the turns ratio:

Working Principle of a Transformer:
A transformer works on the principle of mutual induction. It consists of two coils: the primary coil and the secondary coil, wound on a common iron core. When an alternating current is passed through the primary coil, it creates a changing magnetic field, which induces a voltage in the secondary coil. The voltage ratio between the primary and secondary coils is proportional to the ratio of the number of turns in each coil. For an ideal transformer, the input power is equal to the output power. The voltage and current are related by the following equations:
Where:
- and are the voltages in the primary and secondary coils,
- and are the number of turns in the primary and secondary coils,
- and are the currents in the primary and secondary coils.
Given: - Number of turns ratio ,
- Input voltage ,
- Output current .
Step 1: Calculate the current in the primary coil.
Using the current ratio equation:
Thus, the current in the primary coil is:
So, the current in the primary coil is .
Step 2: Calculate the output power.
The output power is given by:
From the voltage ratio, we can find the secondary voltage:
Thus, the output power is:
Thus, the output power is .