# Episode 116: Using energy and power equations

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

**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 = IV and V = IR and deduce

P = I^{2}R = V^{2}/R. Work towards completing a summary sheet like the one below in the remaining time.

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 = V^{2} / R = I^{2} 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 energy (not charge or current or voltage).
- The electricity companies use a non-SI unit, the kWh, to calculate our bills.
- You could start by showing that domestic appliances transfer large numbers of joules of electrical energy.

(e.g. a 100W lamp illuminated for 10 hours transfers 3 600 000 J of electrical energy to heat and light). 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 = 1000W ´ 3600s = 3 600 000 J

To calculate the cost of electrical energy, 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 electrical energy to heat (e.g. immersion heaters, electric cookers, electric showers).

**Download this episode**Episode 116: Using energy and power equations (Word, 65 KB)