Question

For the given circuit, comment on the type of transformer used.

A. Step-down transformer
B. Auxiliary transformer
C. Step-up transformer
D. Autotransformer

Answer 1

Hint: It is important to know about the transformer and its types. It is a device that transfers the electric energy from one AC circuit to one or more other AC circuits, either increasing or decreasing the voltage. Basically, there are two types of transformers : step-up transformer and step-down transformer. By considering this, let's answer the question.

Complete step by step solution:

Image: A transformer

The step-up transformer is one that increases the voltage from the primary winding to the secondary winding, thereby increasing the output voltage i.e., \[{V_0} > {V_i}\]. Similarly, the step-down transformer is one that decreases the voltage from the primary winding to the secondary winding, thereby decreasing the output voltage i.e., \[{V_0} < {V_i}\].

In the question, they have given that the input voltage given to the transformer as \[{V_i} = 220V\], the output power as \[{P_0} = 60W\], the load current \[{i_L} = 0.11A\]. Now, in order to find which type of transformer it is we need to find whether \[{V_0} > {V_i}\] or \[{V_0} < {V_i}\].
The formula for the power is given as,
\[P = V \times I\]
By the second circuit, we can write it as,
\[{P_0} = {V_0} \times {I_0}\]
Here they have given the value of \[{P_0}\] and \[{I_0}\]...........(\[{I_0} = {I_L}\])

Rearranging the above equation for \[{V_0}\] we get,
\[{V_0} = \dfrac{{{P_0}}}{{{I_0}}}\]
\[\Rightarrow {V_0} = \dfrac{{60}}{{0.11}}\]
\[ \therefore {V_0} = 545.45V\]
Now we can compare the values of \[{V_0}\] and \[{V_i}\] that, the input voltage,\[{V_i} = 220V\] and the output voltage, \[{V_0} = 545.45V\]. Therefore, \[{V_0} > {V_i}\] which concludes that it is a step-up transformer.

Hence, Option C is the correct answer.

Note:Transformers are used in the power transmission of electric energy. The step-up and step-down transformers depend on the windings of the primary and secondary coil and the transformer’s turn ratio.