6.4 Energy transfers and the national grid — Learn

Prerequisites: Section 6.1, especially $Q = It$ and $V = IR$ ; Chapter 1, especially power, energy stores and energy transfers; Chapter 2, work done.

By the end of this section you can: use the equations $P = VI$ , $P = I^2R$ , $E = Pt$ and $E = QV$ ; describe how domestic appliances transfer energy; and explain why the National Grid transfers power at high potential difference.

1. Power in an electrical circuit

Power is the rate at which energy is transferred. It is measured in watts (W). One watt is one joule each second.

When charge flows through a component, work is done on the component. The energy is transferred from the electrical supply to another store. In a motor, the energy goes to the kinetic store. In a heater, it goes to the thermal store.

The power transferred by a device depends on the potential difference across it and the current through it.

P = VI

where $P$ is the power in watts, $V$ is the potential difference in volts and $I$ is the current in amperes.

The same power can also be found from the current and the resistance.

P = I^2R

where $R$ is the resistance in ohms. This form is useful when you know the current and the resistance, but not the potential difference.

2. Energy transferred

The total energy transferred depends on the power and on how long the device is switched on.

E = Pt

where $E$ is the energy transferred in joules, $P$ is the power in watts and $t$ is the time in seconds.

There is a second equation, which uses the charge that flows.

E = QV

where $Q$ is the charge flow in coulombs and $V$ is the potential difference in volts. The two energy equations give the same answer, because $Q = It$ and $P = VI$ .

3. Worked examples

Worked example 1. A heater is connected to the 230 V mains supply and takes a current of 5.0 A. Calculate its power.

\begin{aligned} P &= VI \\ &= 230 \times 5.0 \\ &= 1150\,\text{W} \end{aligned}

Worked example 2. A current of 2.0 A flows through a 15 $\Omega$ resistor. Calculate the power transferred to the resistor.

\begin{aligned} P &= I^2R \\ &= 2.0^2 \times 15 \\ &= 4.0 \times 15 \\ &= 60\,\text{W} \end{aligned}

Worked example 3. The heater of Worked example 1 is switched on for 30 minutes. Calculate the energy it transfers.

\begin{aligned} t &= 30 \times 60 = 1800\,\text{s} \\ E &= Pt \\ &= 1150 \times 1800 \\ &= 2\,070\,000\,\text{J} \\ &= 2.1 \times 10^6\,\text{J} \end{aligned}

Worked example 4. A charge of 9000 C flows through the heater at a potential difference of 230 V. Calculate the energy transferred.

\begin{aligned} E &= QV \\ &= 9000 \times 230 \\ &= 2\,070\,000\,\text{J} \\ &= 2.1 \times 10^6\,\text{J} \end{aligned}

Both methods give the same energy, as they must.

4. Domestic appliances

Every appliance is designed to transfer energy usefully. The table shows two examples.

Appliance	Energy transfer	Power rating
Electric kettle	Electrical to thermal, in the heating element	About 3000 W
Electric motor	Electrical to kinetic, in the motor	About 500 W

A higher power rating means more energy is transferred each second. A 3000 W kettle transfers the same energy in one minute as a 500 W motor transfers in six minutes. The energy transferred depends on the power and on the time.

5. The National Grid

The National Grid is a system of cables and transformers that links power stations to consumers. Electrical power is transferred from the power stations at a very high potential difference, and then transferred at a much lower potential difference in each locality for domestic use.

Step-up transformers increase the potential difference from the power station to the transmission cables. Step-down transformers then decrease it for homes and businesses.

The National Grid is an efficient way to transfer energy because it uses a high potential difference. For a given power, a higher potential difference means a lower current, because $P = VI$ . A lower current means less energy is transferred to the thermal store of the cables, because the power wasted in the cables is $P = I^2R$ . Keeping the current low keeps the wasted power small.

6. Power, time and energy

The figure shows a device of a chosen power running for a chosen time. You can change both the power and the time.

Predict first. Do not move the sliders yet. Write down your answers.

Which transfers more energy: a 0.10 kW lamp for 30 minutes, or a 2.0 kW heater for 1.0 minute?
If the power doubles and the time stays the same, what happens to the energy transferred?

Test. Move the sliders. Set the power to 0.10 kW and the time to 30 minutes, and note the energy. Then set the power to 2.0 kW and the time to 1.0 minute. Compare the two energies.

Explain. The 0.10 kW lamp transfers more energy than the 2.0 kW heater, because it runs for much longer. Why does the time matter as well as the power? Write your answer in two or three sentences.

Watch out. Power and energy are not the same thing. Power is the rate of energy transfer, measured in watts. Energy is the total transferred, measured in joules. A low-power device left on for a long time can transfer more energy than a high-power device used briefly. Also check the unit of time: $E = Pt$ needs seconds, and $P = I^2R$ squares the current before multiplying by the resistance. Re-check which equation a question needs before you substitute.

7. Progress check

Return to the chapter problem. The cabin heater has a power of 1150 W and runs for 30 minutes.

Calculate the energy the heater transfers.
Explain why the National Grid transfers power at high potential difference rather than at 230 V.

You should now be able to

use $P = VI$ and $P = I^2R$ to find a power;
use $E = Pt$ and $E = QV$ to find an energy transfer;
describe how domestic appliances transfer energy from a supply to a useful store;
explain the link between a power rating and the energy transferred over a time;
describe the National Grid and the job of step-up and step-down transformers;
explain why transferring power at high potential difference is efficient.