Which of the following modes is the most economical method of transmitting electrical power over long distances?

Analyze the question: The question asks which method of transmitting power over long distances wastes the least energy, which makes it the most economical.

Explain the concept: Power transmitted is P = IV. Power lost as heat in the transmission cables is P_loss = I²R, where R is the resistance of the cables.

To reduce the loss, we must reduce the current I. Because P = IV, we can still deliver the same power at a lower current if we raise the voltage.

Transformers make this easy with alternating current. A step-up transformer raises the voltage (and lowers the current) at the power station. A step-down transformer lowers the voltage again near the consumers. This is not easy to do with direct current, which is why AC is preferred.

Solution (example): Suppose 100 kW is to be sent through cables of resistance 10 Ω.

• At 1,000 V: I = 100,000 / 1,000 = 100 A, so loss = 100² × 10 = 100,000 W. All the power is lost.
• At 100,000 V: I = 100,000 / 100,000 = 1 A, so loss = 1² × 10 = 10 W. Almost nothing is lost.

So high voltage means low current, which means very little heat loss.

Checking the options:

• A: Low voltage and high current gives a large I²R loss. ✗
• B: High current gives a large I²R loss, even with high voltage. ✗
• C: AC at high voltage and low current gives minimal loss and works with transformers. ✓
• D: DC at low voltage and high current gives a large loss and cannot be easily stepped up. ✗

Answer: C. Alternating current at high voltage and low current

Exam tip: Remember "High Voltage, Low Loss". Power loss depends on I², so any option with high current is wrong. For this question, look for "high voltage, low current" in the options.