E3: Electrical energy — B level

Energy is lost in power lines. This is because electrical cables all have a small resistance. Electrical energy is converted to heat in them.

The amount of energy lost can be calculated using Ohm’s Law, the power formula, and the energy formula.

V = IR

P = VI

E = Pt

Imagine a transmission line with these characteristics:

• Current rating: 1000A. This is the largest current it will carry.
• Resistance: 0.5𝛺.

Assume that the transmission line is carrying 1000A all the time. Calculate:

1. The voltage drop along the transmission line (in Volts).
2. The power being lost as heat along the transmission line (in Watts).
3. The energy lost as heat in one day.

In real transmission lines, the voltage is increased to reduce this wasted energy. This reduces the current.

Let’s imagine that a transformer increases the voltage 5x. The numbers are now:

• Current rating: 200A. This is the largest current it will carry.
• Resistance: 0.5𝛺.

Assume that the transmission line is carrying 200A all the time. Calculate:

1. The voltage drop along the transmission line (in Volts).
2. The power being lost as heat along the transmission line (in Watts).
3. The energy lost as heat in one day.