Question

A thermal power plant produces electric power of $600kW$ at $4000V$, which is to be transported to a place $20km$ away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with power factor unity. All the currents and voltages mentioned are rms values.
In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is $1:10$. If the power to the consumers has to be supplied at $200V$, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is
$A)200:1$
$B)150:1$
$C)100:1$
$D)50:1$

Answer 1

For an ideal transformer with power factor unity, ratio of secondary voltage to primary voltage is equal to the ratio of no. of turns in the secondary to the no. of turns in the primary. Hence, use this equation to find the primary voltage. Then substitute the calculated primary voltage and the given secondary voltage in the same equation to find the secondary to primary no. of turns ratio of the step down transformer.

Complete answer:
For an ideal transformer with power factor unity,
$\dfrac{{{V}_{s}}}{{{V}_{P}}}=\dfrac{{{N}_{s}}}{{{N}_{P}}}$
Where,
${{V}_{P}}$ is the primary voltage
${{V}_{s}}$ is the secondary voltage
${{N}_{P}}$ is the number of turns in the primary
${{N}_{s}}$ is the number of turns in the secondary
It is given that, number of turns in the primary to that in the secondary in the step-up transformer is in the ratio $1:10$. Then,
$\dfrac{{{N}_{P}}}{{{N}_{s}}}=\dfrac{1}{10}$ ------- 2
${{V}_{s}}=4000V$------- 3
Substitute 2 and 3 in equation 1. We get,
$\dfrac{4000}{{{V}_{p}}}=\dfrac{1}{10}$
${{V}_{p}}=4000\times 10=40000V$
To find the ratio of the step down transformer with ${{V}_{p}}=40000V$ and ${{V}_{s}}=200V$, substitute these values in equation 1.
$\dfrac{{{V}_{s}}}{{{V}_{P}}}=\dfrac{200}{40000}=\dfrac{1}{200}$
Then,
$\dfrac{{{N}_{s}}}{{{N}_{P}}}=\dfrac{1}{200}$
Therefore, the number of turns in the primary to that in the secondary in the step-down transformer is$200:1$.

So, the correct answer is “Option A”.

Note:
We can use the same transformer as a step-up or a step-down transformer. It depends on which way; it is connected in the circuit. If input supply is given on the high voltage winding, then it becomes a step-down transformer. Alternately, if the input supply is provided on the low voltage winding, the transformer becomes a step-up one.