Question

A transformer converts 200 V into 2000 V ac. Calculate the number of turns in the secondary if the primary has 10 turns.

Answer 1

Hint:Number of turns in the coil has an inverse relation with voltage across the coil. It is expressed as $V \propto \dfrac{1}{N}$.

Complete step by step solution:We know from the question that the voltage across primary coil is ${V_p} = 200\;{\rm{V}}$ , the voltage across secondary coil is ${V_s} = 2000\;{\rm{V}}$ and the number of turns in primary coil is ${N_p} = 10$

We know that the relationship between the voltage across coil and number of turns in the coil is inversely proportional. We have,
$V \propto \dfrac{1}{N}$

We can write the above equation in terms of primary and secondary coil, we have
$\dfrac{{{V_p}}}{{{V_s}}} = \dfrac{{{N_s}}}{{{N_p}}}$
Now we substitute the values $200\;{\rm{V}}$ as ${V_p}$, $2000\;{\rm{V}}$ as ${V_s}$ and $10$ as ${N_p}$ in the above expression, we get,
$
\dfrac{{200\;{\rm{V}}}}{{2000\;{\rm{V}}}} = \dfrac{{{N_s}}}{{10}}\\
{N_s} = 100\;{\rm{turns}}
$

Hence, the number of turns in the secondary coil of the transformer is 100 turns.

Additional Information:Different operations take place in transformers: transmission of electricity from one circuit to another, transmission of electric power by electromagnetic induction and two circuits are connected with mutual induction.
Transformer is used to transmit the electricity with the help of long wires and it is also used as a voltage regulator. Transformers having two or more than two secondaries are used in television and radio receivers.

Note:The voltage transformation ratio is expressed as:
$\dfrac{{{V_p}}}{{{N_p}}} = \dfrac{{{V_s}}}{{{N_s}}} = k$
Here, \[k\] is called the voltage transformation ratio.
When ${N_s}$ is greater than ${N_p}$, $k > 1$ it is known as a step-up transformer.
When ${N_s}$ is lower than ${N_p}$, $k < 1$ it is known as a step-down transformer.