Question

In step-up transformers the output voltage is $11\,KV$ and the input voltage is $220\,V$. The ratio of number of turns of secondary to primary is
$A)\,\,20:1 \\\ B)\,\,22:1 \\\ C)\,\,50:1 \\\ D)\,\,1:50 \\\$

Answer 1

In the question the input voltage and output voltage of the step-up transformer is given. Substituting the known values in the equation of turns ratio we get the value of the number of turns of secondary to primary coils.

Formula used:
The expression for finding the number of turns in the coil is,
$\dfrac{{{i_p}}}{{{i_s}}} = \,\dfrac{{{v_p}}}{{{v_s}}}$
Where ${i_p}$ be the number of turns in the primary coil, ${i_s}$be the number of turns in the secondary coil, ${v_p}$ be the potential of primary voltage and ${v_s}$ be the potential of secondary voltage.

Complete step by step solution:
Given that,
Potential of primary voltage ${v_p}\, = \,220\,V$
Potential of secondary voltage ${v_s}\, = \,11\,KV$
Convert the secondary voltage in terms of V, we get
Potential of secondary voltage ${v_s}\, = \,11000\,V$
Number of turns in the primary coil ${i_{p\,}}\, = \,?$
Number of turns in the secondary coil ${i_s}\, = \,?$
$\dfrac{{{i_p}}}{{{i_s}}} = \,\dfrac{{{v_p}}}{{{v_s}}}...........\left( 1 \right)$
Substitute the known values in the equation $\left( 1 \right)$
$\dfrac{{{i_p}}}{{{i_s}}} = \,\dfrac{{220}}{{11000}}$
Simplify the above equation we get
$\dfrac{{{i_p}}}{{{i_s}}} = \,\dfrac{1}{{50}}$
Convert the above equation in terms of secondary to primary coils, we get
$\dfrac{{{i_s}}}{{{i_p}}} = \,\dfrac{{50}}{1}$
Therefore. the number of turns of the secondary to primary coils is $50:1$

Hence, from the above options, option C is correct.

Note: In the question, step up transformer is used. It states that the voltage increases the voltage by decreasing the current. In the question we need to find the number of turns in the secondary to primary coil. So reciprocal the values we get the value of secondary to primary coils. we know that the power is proportional to the voltage and current. In the question we use the equation called ratio of transformation. This is also a turns ratio.