Question

A transformer has $500$ turns of the primary winding and $10$ turns of the secondary winding. Determine the secondary voltage if the secondary circuit is open and the primary voltage is $120\,{\text{V}}$ .

Answer 1

First of all, we will apply the formula which relates the ratio of voltages of secondary and primary circuit to the ratio of number of windings of the respective circuits. We will substitute the required values and manipulate accordingly to obtain the result.

Complete step by step answer:
In the given problem, we are supplied with the following data:
The total number of turns of the primary winding is $500$ turns.
The number of turns of the secondary winding is $10$ turns.
The voltage in the primary winding is $120\,{\text{V}}$ .
We are asked to find the voltage in the secondary winding if the secondary circuit is open.

To begin with, we will use the fact about a transformer, which says that the ratio of the voltages on the secondary circuit and the primary circuit is equal to the ratio of the number of turns of secondary winding and primary winding.
Mathematically, we can write as:
$\dfrac{{{v_2}}}{{{v_1}}} = \dfrac{{{N_2}}}{{{N_1}}}$ …… (1)
Where,
${v_2}$ indicates the voltage in the secondary circuit.
${v_1}$ indicates the voltage in the primary circuit.
${N_2}$ indicates the number of turns in the secondary winding.
${N_1}$ indicates the number of turns in the primary winding.

We will now rearrange the equation (1) and we get:
${v_2} = \dfrac{{{N_2}}}{{{N_1}}} \times {v_1}$ …… (2)
Now, substituting the required values in the equation (2) we get:
{v_2} = \dfrac{{{N_2}}}{{{N_1}}} \times {v_1} \\\ \implies {v_2} = \dfrac{{10}}{{500}} \times 120\,{\text{V}} \\\ \therefore {v_2} = 2.4\,{\text{V}} \\\
Hence, the secondary voltage if the secondary circuit is open is $2.4\,{\text{V}}$ .

Additional Information:
There are various types of transformers, step-up and step-down transformers, power transformers. These are the electrical devices which transfer electrical energy from one circuit to another circuit or even multiple circuits.

Note:
The transformers work under the main principle of windings in the circuits. Higher the number of turns in the circuit, higher is the voltage generated. Primary winding converts the electrical power to a magnetic field while the secondary winding converts the varying magnetic field into electrical power which produces the required voltage as output.