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A thermal power station generates electrical power of 600 kW at 4000 V, to be delivered to consumers located 20 km away. Transmission can be done either directly through a high-current cable or via a step-up transformer at the plant and a step-down transformer at the consumer end (cable purely resistive, transformers ideal, power factor unity, all values rms). Using transformers, the step-up transformer at the plant has a primary-to-secondary turns ratio of 1: 10. If the consumers must receive power at 200 V, what is the primary-to-secondary turns ratio of the step-down transformer?

1. 200: 1
2. 150: 1
3. 100: 1
4. 50: 1

Correct answer: 200: 1

Solution

Step-up transformer raises 4000 V by a factor of 10 (turns ratio 1:10) to 40000 V on the transmission line. The step-down transformer must reduce this 40000 V to 200 V for the consumers. The turns ratio of the step-down transformer equals the voltage ratio: 40000/200 = 200, i.e. 200: 1.

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