Question

A transformer of efficiency $90\%$ has turns ratio 1:10. If the voltage across the primary is 220V and current in the primary is 0.5A, then the current in secondary is
A.)5.5A
B.)5A
C.)4A
D.)4.5A

Answer 1

Hint: Efficiency of transformer is the ratio of real output power and real input power. Students must know the formula of power in the form of voltage and current. Also, the relation between turn ratio and voltage ratio of the transformer helps to solve this question accurately.

Complete step-by-step answer:
Let ${{N}_{p}}$ and ${{N}_{S}}$ be the number of turns of primary and secondary respectively. ${{I}_{P}}$ and ${{I}_{S}}$ be the current in primary and secondary respectively. Also consider, ${{V}_{P}}$ and ${{V}_{S}}$ be the voltage of primary and secondary respectively.
E be the efficiency of a transformer.
Here, it is given that efficiency of the transformer is $E=90%$

Turns ratio of the transformer is, $\dfrac{{{N}_{S}}}{{{N}_{P}}}=\dfrac{1}{10}$
Voltage of the primary is, ${{V}_{P}}=220V$
Current in the primary is ${{I}_{P}}=0.5A$

We know the formula for efficiency of a transformer as the ratio of the output power to the input power.

$E=\dfrac{{{I}_{S}}{{V}_{S}}}{{{I}_{P}}{{V}_{P}}}$ …..(1)
But here we have not given the value of V_S. So first we do calculations for V_S.
The relation between N and V is,

$\begin{align}
  & \dfrac{{{N}_{S}}}{{{N}_{P}}}=\dfrac{{{V}_{S}}}{{{V}_{P}}} \\
 & \dfrac{1}{10}=\dfrac{{{V}_{S}}}{220} \\
 & {{V}_{S}}=22V \\
\end{align}$
                                                                        …………(2)
Substituting value from equation (2) in equation (1), we get,
$\dfrac{90}{100}=\dfrac{{{I}_{S}}\times 22}{0.5\times 220}$
Solving the obtained equation, we get final solution,

${{I}_{S}}=4.5A$

Hence, the current in secondary is ${{I}_{S}}=4.5A$
The correct option is D.

Note: There is a possibility of mistake in the formula of efficiency of transformer for the input and output power. It is the ratio of power of secondary to that of the primary. If it gets exchanged then the final answer will be wrong.
For the step-up and the step-down transformer, the equations are the same for both the types of transformer. Only difference is in the number of turns in the primary coil and the secondary coil. In a step-up transformer the number of turns in the secondary is more than the primary and in a step-down transformer the number of turns in the primary is more than in the secondary.