Question

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 200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is

Answer 1

The ratio of the number of turns in the primary to that in the secondary in the step-down transformer is $V_{p2} : 200$, where $V_{p2}$ is the voltage transmitted. Without the value of $V_{p2}$, a specific numerical ratio cannot be determined.

Answer 2

Let $N_{p1}$ and $N_{s1}$ be the number of turns in the primary and secondary of the step-up transformer, respectively. Given $N_{p1} : N_{s1} = 1 : 10$. For an ideal transformer, the voltage ratio is equal to the turns ratio: $\frac{V_{s1}}{V_{p1}} = \frac{N_{s1}}{N_{p1}} = 10$. This means the voltage is stepped up by a factor of 10. Let the input voltage to the step-up transformer be $V_{p1}$ and the output voltage (transmitted voltage) be $V_{s1}$. So, $V_{s1} = 10 \times V_{p1}$.

This transmitted voltage $V_{s1}$ becomes the primary voltage of the step-down transformer, so $V_{p2} = V_{s1}$. The power is supplied to consumers at 200 V, which is the secondary voltage of the step-down transformer, so $V_{s2} = 200$ V.

We need to find the ratio of the number of turns in the primary to that in the secondary for the step-down transformer, which is $N_{p2} : N_{s2}$. Using the voltage-turn ratio relationship for an ideal transformer: $\frac{N_{p2}}{N_{s2}} = \frac{V_{p2}}{V_{s2}}$.

Substituting the known values: $\frac{N_{p2}}{N_{s2}} = \frac{V_{p2}}{200}$.

Since $V_{p2} = V_{s1} = 10 \times V_{p1}$, the ratio can also be written as: $\frac{N_{p2}}{N_{s2}} = \frac{10 \times V_{p1}}{200} = \frac{V_{p1}}{20}$.

The problem does not provide the initial voltage $V_{p1}$ or the transmitted voltage $V_{p2}$. Therefore, a specific numerical ratio for the step-down transformer cannot be determined from the given information. The ratio of turns in the primary to that in the secondary in the step-down transformer is $V_{p2} : 200$, where $V_{p2}$ is the voltage transmitted at high tension.