Question

A transformer has 500 turns in its primary and 1000 turns in its secondary winding. The primary voltage is 200V and the load in the secondary is $100\Omega $. Calculate the current in the primary, assuming it to be an ideal transformer.
$\begin{align}
  & A.25A \\
 & B.45A \\
 & C.8A \\
 & D.22A \\
\end{align}$

Answer 1

Hint: A transformer turns ratio is defined as the ratio of the number of turns in the primary winding to the number of turns in the secondary winding. This is given by the equation,
${{T}_{R}}=\dfrac{{{N}_{P}}}{{{N}_{S}}}$
This ratio should be equivalent to the ratio of voltage in the primary winding to the voltage of the secondary winding. This can be written as,
$\dfrac{{{V}_{P}}}{{{V}_{S}}}$
This will help in solving this question.

Complete step by step solution:
As the transformer is a general and a common linear device, a ratio will be existing between the number of turns of the primary coil and the number of turns of the secondary coil. This ratio is known as the ratio of transformation. It is more commonly known as the transformers turn ratio.

As in the case of normal rotation,
$\dfrac{{{V}_{S}}}{{{V}_{P}}}=\dfrac{{{N}_{S}}}{{{N}_{P}}}$
Where ${{V}_{S}}$ the voltage in the secondary coil, ${{V}_{P}}$ the voltage in the primary coil, ${{N}_{S}}$ number of turns in the secondary coil, and ${{N}_{P}}$ the number of turns in the primary coil.
Rearranging this equation will give,
${{V}_{S}}={{V}_{P}}\times \dfrac{{{N}_{S}}}{{{N}_{P}}}$
Substituting the given data in this equation will give,
$\begin{align}
  & {{V}_{S}}=200V\times \dfrac{1000}{500} \\
 & \,{{V}_{S}}=400V \\
\end{align}$
As there is a load resistance $100\Omega $ placed in the secondary circuit, the current in the secondary circuit is given as,
${{i}_{S}}=\dfrac{{{V}_{S}}}{{{R}_{S}}}=\dfrac{400V}{100\Omega }=4A$
As we know, the input power and the output power in an ideal transformer is equivalent.
Therefore
${{V}_{S}}\times {{i}_{S}}={{V}_{p}}\times {{i}_{p}}$
From this relation, we can obtain the current flowing in the primary coil,
That is given by rearranging these equations,
${{i}_{p}}=\dfrac{{{V}_{S}}}{{{V}_{p}}}\times {{i}_{S}}$
Substituting the value in this equation will give,
${{i}_{p}}=\dfrac{400V}{200V}\times 4A$
Simplifying this equation will give,
${{i}_{p}}=2\times 4A=8A$
Therefore the correct answer is given as option C.

Note: A transformer is basically electrical equipment used to convert the electrical energy from one electrical circuit to the other. Transformers are helpful in increasing low AC voltages or decreasing high AC voltages. These are known as step-up transformers and step down transformers respectively.