## Episode 116: Using energy and power equations

Lesson for 16-19

- Activity time 65 minutes
- Level Advanced

In this episode, students develop their competence in using the equations for power and energy, in an electrical context.

Lesson Summary

- Discussion: Equations for power (15 minutes)
- Student questions: Using equations (30 minutes)
- Discussion: Paying for electricity (10 minutes)
- Student activity: Calculating an electricity bill (10 minutes)

#### Discussion

It is worth spending 5 minutes deriving different versions of the equations, i.e. start from
*P* = *I* × *V*
and
*V* = *I* × *R*
to deduce
*P* = *I*^{ 2} × *R*
and
*P* = *V*^{ 2}*R*.

Now would be a good time to summarise all of these in the remaining time. Work towards completing a summary sheet like the one below.

Quantity | Symbol | SI unit | Comments | Equations |
---|---|---|---|---|

Potential difference | V | Volt (V) | Also use mV and kV | V = W / Q |

Charge | Q | Coulomb (C) | Q = It | |

Current | I | Amp (A) | Also use mA | |

Energy | E or W | Joule (J) | Also use kJ, MJ | |

Power | P | Watt (W) | Also use mW, kW, MW | P = W / t, P = I V = V2 / R = I2 R |

Resistance | R | Ohm (W) | Also use kW | R = V / I |

Time | t | Second (s) |

#### Student questions

Students can now work on a series of exercises. These could be set as a homework activity but there is something to be said for letting them work through the problems in class in front of you and pausing to go through solutions every now and again. This will identify problems quickly (and deal with them).

Episode 116-1: The algebra of power (Word, 22 KB)

#### Discussion

Paying for electricity: this should be revision of work covered at a previous stage in your school or college. The main points to get across are that:

- We pay for the electrical work done by our electricity supply (not charge or current or voltage). Usually this is an energy source such as a fuel at a power station but the cost also includes the production costs (infrastructure and maintanance).
- The electricity companies use a non-SI unit, the kWh, to calculate our bills.
- You could start by showing that domestic appliances have a high power rating (often in kilo watts).

(e.g. a 100 W lamp illuminated for 10 hours transfers 3 600 000 J of energy to the surroundings). Define the kilowatt-hour (kWh) as the amount of energy transferred by a 1 kW appliance operating continuously for 1 hour.

Amount of energy in kWh is then just:

energy / kWh = power / kW) × time / h)

so 1 kWh = 1000 W × 3600 s

1 kWh = 3 600 000 J

To calculate the cost of electricity, multiply the energy transferred (kWh) by the cost per kWh (p).

#### Student activity

At this point it would be helpful to show them an electricity meter and a bill and then to get them to calculate the costs of running common appliances. This will emphasize the large power of devices that transfer energy by heating (e.g. immersion heaters, electric cookers, electric showers).