Question

A power transmission line feeds input power at $2300{\text{V}}$ to a step down transformer with its primary windings having ${\text{4000}}$ turns. What should be the number of turns in the secondary in order to get output power at $230{\text{V}}$?

Answer 1

Hint: The voltage at the either side of a transformer is proportional to the number of turns at that side. Therefore, the ratio of the voltages at the primary and the secondary side of a transformer is equal to the ratio of the number of turns of the primary and the secondary windings. Using this relation, we can substitute the given values and can determine the required value of the number of turns in the secondary.

Formula used: The formula used to solve this question is given by
$\dfrac{{{V_1}}}{{{N_1}}} = \dfrac{{{V_2}}}{{{N_2}}}$, here ${V_1}$ and ${N_1}$ are the voltage and the number of turns at the primary of a transformer, and ${V_2}$ and ${N_2}$ are the corresponding values at the secondary.

Complete step-by-step solution:
Let the number of turns in the primary and the secondary windings of the given transformer be ${N_1}$ and ${N_2}$ respectively. Also, let ${V_1}$ and ${V_2}$ be the respective values of the voltages at the primary and the secondary of the transformer.
According to the question, we have
${V_1} = 2300{\text{V}}$................(1)
${V_2} = 230{\text{V}}$ ………...(2)
Also,
${N_1} = 4000$ …………………..(3)
We know that for a transformer we can write
$\dfrac{{{V_1}}}{{{N_1}}} = \dfrac{{{V_2}}}{{{N_2}}}$
Substituting (1), (2) and (3) in the above equation we get
$\dfrac{{2300}}{{4000}} = \dfrac{{230}}{{{N_2}}}$
$ \Rightarrow {N_2} = 230 \times \dfrac{{4000}}{{2300}}$
On solving we get
${N_2} = 400$

Hence, for the given value of the output voltage, the number of turns in the secondary of the given transformer is equal to $400$.

Note: A step down transformer is used to decrease the high voltage applied at the primary side to the low voltage. For this purpose it has less number of turns at the secondary side than at the primary side. Since the given transformer is stepped down, confirm that the number of turns at the secondary that you have got must be less than the number of turns at the primary.