Question

In a primary coil 5 A current is flowing on 220 volts. if the secondary coil produces 2200 V voltage. then the ratio of the number of turns in the secondary coil and the primary coil will be:
A). $1:10$
B). $10:1$
C). $1:1$
D). $11:1$

Answer 1

Hint: The ratio of voltages in the primary coil and the secondary coil of the transformer is always constant. Similarly, the ratio of the current in the primary coil and the secondary coil of the transformer is again a constant value. These two ratios are what we call the turns ratio.
Formula Used:
$\dfrac{{{V}_{2}}}{{{V}_{1}}}=\dfrac{{{N}_{2}}}{{{N}_{1}}}$

Complete step-by-step solution:
In a transformer, the ratio of voltage occurring on the primary to that of the voltage occurring in the secondary is a constant value, which is equal to the ratio of turns of coils present in the primary coil to that of the turns present in the secondary coil. This ratio of voltages has a relation with the ratio of the currents occurring in the primary and the secondary coils.
This relation is often termed as transformation ratio and is given by:
$\dfrac{{{V}_{2}}}{{{V}_{1}}}=\dfrac{{{N}_{2}}}{{{N}_{1}}}$ -----(i)
The ratio for the currents is given by:
$\dfrac{{{I}_{1}}}{{{I}_{2}}}=\dfrac{{{N}_{2}}}{{{N}_{1}}}$ ------(ii)
Here, $\dfrac{{{N}_{2}}}{{{N}_{1}}}$ is referred to as the turns ratio. This can easily be found using equation (i) as:
$\dfrac{{{N}_{2}}}{{{N}_{1}}}=\dfrac{2200}{220}$
$\Rightarrow {{N}_{2}}:{{N}_{1}}=10:1$
Hence, the correct option is (b)
Additional Information
From equation (i) and (ii), we get the relation between ratio of voltages and currents as:
$\dfrac{{{V}_{2}}}{{{V}_{1}}}=\dfrac{{{I}_{1}}}{{{I}_{2}}}$ ----(iii)
Now, putting the respective values mentioned in the question in equation (iii):
$\dfrac{2200}{220}=\dfrac{5}{{{I}_{2}}}$
$\Rightarrow {{I}_{2}}=0.5A$

Note: Notice carefully that the turns ratio is the ratio of the voltages on the secondary side to the primary side. On the contrary, the ratio of the primary current to that of the secondary current is termed as turns ratio. Take the ratios carefully while answering the question.