Question

A step up transformer operates on a 230V line and supplies to a load 2A. The ratio of primary to secondary winding is $1:25$ . Determine the primary current.
A.8.8 A
B.12.5 A
C.25 A
D.50 A

Answer 1

Hint: Define the working of a transformer. Obtain the mathematical expressions relating the number of turns in the primary and secondary to the current in primary and secondary. Since, the winding ratio and the secondary current is given, by putting these values in the equation obtained, we can get the required answer.

Complete answer:
A transformer which can increase the voltage from primary to secondary is called a step-up transformer. A step-up transformer converts low voltage to high voltage and high current to low current. In the process the total power of the transformer remains the same. In the step-up transformer the number of turns in the secondary coil is more than the primary coil.
 We can define the relation between the number of turns and the voltages as,
$\dfrac{{{N}_{p}}}{{{N}_{s}}}=\dfrac{{{V}_{p}}}{{{V}_{s}}}=\dfrac{{{I}_{s}}}{{{I}_{p}}}$
We have a step-up transformer.
Given, the ratio of the primary to secondary winding is $1:25$.
So, we can write,
$\dfrac{{{N}_{p}}}{{{N}_{S}}}=\dfrac{1}{25}$
Again, for a transformer we can obtain the relation between primary and secondary winding to primary and secondary current as,
$\dfrac{{{N}_{p}}}{{{N}_{s}}}=\dfrac{{{I}_{s}}}{{{I}_{p}}}$
So, we can write that,
$\dfrac{{{N}_{p}}}{{{N}_{S}}}=\dfrac{1}{25}=\dfrac{{{I}_{s}}}{{{I}_{p}}}$
So, we can write,
$\begin{align}
  & \dfrac{{{I}_{s}}}{{{I}_{p}}}=\dfrac{1}{25} \\
 & {{I}_{p}}=25{{I}_{s}} \\
\end{align}$
Given the value of the secondary or load current is 2A.
Putting this value on the above equation we get that,
$\begin{align}
  & {{I}_{p}}=2A\times 25 \\
 & {{I}_{p}}=50A \\
\end{align}$
So, the primary current will be 50A.
The correct option is (D).


Note: A step-down transformer converts high voltage to low voltage and low current to high current. For a step-down transformer the number of turns in the secondary is less than the number of turns in the primary.
For both the step-up and step-down transformer the relations are the same. The only difference is in the number of turns in the coils and it changes the working of the transformers.