A power station delivers 100 kW of electrical power to a distant village through transmission cables with a total resistance of 5.0 Ω. In scheme A the power...

Marking Scheme

• (a) I = P / V = 100 000 / 1000 [1]; = 100 A [1]
• (b) P_lost = I²R = 100² × 5.0 [1]; = 50 000 W (50 kW) [1]
• (c) I = 100 000 / 10 000 = 10 A [1]
• (d) P_lost = 10² × 5.0 = 500 W (0.50 kW) [1]
• (e) Transmitting at higher voltage means lower current for the same power [1]; since P_lost = I²R, a lower current greatly reduces energy wasted as heat [1]

Explanation

(a) The power station delivers 100 kW at 1000 V. Using P = IV:

\( I = \frac{P}{V} = \frac{100\,000}{1000} = 100 \text{ A} \)

(b) The power dissipated in the cable resistance is:

\( P_{lost} = I^2 R = 100^2 \times 5.0 = 50\,000 \text{ W} = 50 \text{ kW} \)

This is 50% of the total power - half the generated power is wasted as heat in the cables.

(c) In scheme B the voltage is stepped up to 10 000 V, so:

\( I = \frac{100\,000}{10\,000} = 10 \text{ A} \)

The current is 10 times smaller than in scheme A.

(d) \( P_{lost} = I^2 R = 10^2 \times 5.0 = 500 \text{ W} = 0.50 \text{ kW} \)

This is only 0.5% of the total power.

(e) For the same power delivered, increasing the transmission voltage by a factor of 10 reduces the current by a factor of 10. Since cable losses depend on I²R, reducing I by 10 reduces the power loss by a factor of 100 (from 50 kW to 0.50 kW). This is why the National Grid uses very high voltages (hundreds of kV) for long-distance transmission. Step-up transformers at the power station increase the voltage, and step-down transformers near consumers reduce it to safe levels.