What is the function of a transformer in an a.c. circuit? How do the input and output power in a transformer compare?

Hint: Study the types of transformers. The transformer works on Faraday’s principle of mutual induction where emf is induced in the secondary coil through the voltage or current flowing through the primary coil. Try to derive the formulas involving different types of transformers.

Formula used:
Voltage across the secondary coil is,
${{V}_{s}}=-{{N}_{s}}\dfrac{d\phi }{dt}$
Voltage across the primary will be,
${{V}_{p}}=-{{N}_{p}}\dfrac{d\phi }{dt}$
Equating the above formulas the formula for a step-down transformer is,
$\dfrac{{{N}_{s}}}{{{N}_{p}}}=\dfrac{{{V}_{s}}}{{{V}_{p}}}$

Complete Step-by-Step solution:
A transformer is a passive electrical device which transfers one electrical circuit to another. It consists of two electrically isolated coils and works Faraday's principle of mutual inductance. It transforms electrical energy to the magnetic energy on the primary side and again from magnetic energy to the electrical energy on the secondary side.
The function of a transformer in a.c. circuit is that, it can step up or step down the alternating voltage but the power remains constant. In a step up transformer the high voltage is transformed to low voltage and in a step up transformer low voltage is transformed into high voltage.
A step-down transformer can be defined as an object which transforms the high voltage and low current to low voltage and high current. The number of turns of wire in the coil on the primary side is high and the number of turns of wire in the coil on the secondary side is less.
Voltage across the secondary coil is,
${{V}_{s}}=-{{N}_{s}}\dfrac{d\phi }{dt}$
Voltage across the primary will be,
${{V}_{p}}=-{{N}_{p}}\dfrac{d\phi }{dt}$
Equating the above formulas the formula for a step-down transformer is,
$\dfrac{{{N}_{s}}}{{{N}_{p}}}=\dfrac{{{V}_{s}}}{{{V}_{p}}}$
Where, ${{N}_{s}}$is the number of turns in the secondary coil;
${{N}_{p}}$ is the number of turns in the primary coil;
${{V}_{s}}$ is the voltage in the secondary and;
${{V}_{p}}$ is the voltage in the primary
Voltage and current are inversely proportional,
${{i}_{p}}{{v}_{p}}={{i}_{s}}{{v}_{s}}$
Power can be defined as, $P=IV$
So, from the above equation we can say that the input and output power of the transformer remains the same. It will be the same if we consider a step up transformer also.

Note: From the above relations we can see that in a step-down transformer voltage will always decrease as voltage and current are inversely proportional.
Again, if the transformer is assumed to be 100 percent efficient the input power and the output power will be equal. So, the wattage will neither increase or decrease.