A thermal power plant produed electric power of 600kW at 4000V, which is to be transported to a place 20 km away form the power plant for consumer's usage. It can be transported either directly with a cable of large current carrying capacity or by sing a combination of step-up and step-down transfprmers at the two ends. THe drawback of the direct transmission is the large energy dissipation. In the method wsing transformers, the dissipatiion is much smaller. In this method a step-up transformers 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 resostive and the transformers are ideal with power factor unity. All the currents and voltagementioned are 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

Options

A. 200
B. 150
C. 100
D. 50

Explanation

To solve the problem step by step, we will analyze the situation involving the thermal power plant, transformers, and the transmission of power.

### Step-by-Step Solution:

1. **Understanding the Power Plant Output:**
- The power plant produces electric power of \( P = 600 \, \text{kW} \) at a voltage of \( V_P = 4000 \, \text{V} \).

2. **Calculating the Current at the Power Plant:**
- The current \( I_P \) at the power plant can be calculated using the formula:
\[ P = V_P \times I_P \]
- Rearranging gives:
\[ I_P = \frac{P}{V_P} = \frac{600 \times 10^3 \, \text{W}}{4000 \, \text{V}} = 150 \, \text{A} \]

3. **Using the Step-Up Transformer:**
- The step-up transformer increases the voltage while decreasing the current. The turns ratio is given as:
\[ \frac{N_P}{N_S} = \frac{1}{10} \]
- This means that the secondary voltage \( V_S \) of the step-up transformer will be:
\[ V_S = 10 \times V_P = 10 \times 4000 \, \text{V} = 40000 \, \text{V} \]

4. **Understanding the Step-Down Transformer:**
- The output voltage required for consumers is \( V_C = 200 \, \text{V} \).
- The primary voltage \( V_{P_{SD}} \) of the step-down transformer is the secondary voltage of the step-up transformer:
\[ V_{P_{SD}} = V_S = 40000 \, \text{V} \]

5. **Finding the Turns Ratio for the Step-Down Transformer:**
- The turns ratio for the step-down transformer can be expressed as:
\[ \frac{N_{P_{SD}}}{N_{S_{SD}}} = \frac{V_{P_{SD}}}{V_C} \]
- Substituting the values:
\[ \frac{N_{P_{SD}}}{N_{S_{SD}}} = \frac{40000 \, \text{V}}{200 \, \text{V}} = 200 \]
- Therefore, the turns ratio of the primary to the secondary of the step-down transformer is:
\[ \frac{N_{P_{SD}}}{N_{S_{SD}}} = 200:1 \]

### Final Answer:
The ratio of the number of turns in the primary to that in the secondary in the step-down transformer is **200:1**.

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