Episode 106: Electrical power

Students may need to be reminded of the idea that power is the rate of doing work (or the rate at which energy is transferred).

Lesson Summary

• Discussion: How to calculate electrical power (15 minutes)
• Student questions: Calculations (30 minutes)
• Discussion: Reviewing progress, checking understanding (30 minutes)

Discussion: How to calculate electrical power

Start with some theory, reinforcing the idea of voltage and using the equations:

Δ E = V ×  Δ Q and Δ Q = I ×  Δ t

to derive Δ E = I × V Δ Q

The rate of doing work is the power:

P =  Δ E Δ t

P = I × V

Discuss the significance of this using familiar examples; e.g. a 100 W lamp connected to 230 V (ac) supply; an electric kettle (about 2.0 kW); power station transmitting 1.0 GW along transmission lines illustrating the need to transmit at high voltage in order to reduce losses due to heating.

Episode 106-1: Lamp lighting (Word, 36 KB)

Student questions: Calculations

These questions, which can be used in class or for homework will give you the opportunity to asses your students’ understanding at the end of this introduction to electric circuits – see the discussion below.

Episode 106-2: The power of a torch bulb (Word, 20 KB)

Episode 106-3: Kinds of the light bulbs (Word, 47 KB)

Episode 106-4: Power of appliances (Word, 59 KB)

Discussion: Reviewing progress, checking understanding

In discussing students’ work on this topic, there are a number of things to look out for. Students may fail to discriminate between terms – current and voltage in particular.

Potential difference (pd) versus voltage

pd has the advantage that it emphasises that we are measuring a change between two different points in an electric circuit (rather than flow at one point).

Electromotive force

(emf) is a term for voltages across sources of electrical supplies (cells or power packs).

Cells becoming discharged

charge is not used up, energy is transferred and, usually, dissipated.

This is a good time to reinforce some other ideas:

Conventional current:

This flows (by definition) from positive to negative around the external circuit (inside the cell chemical reactions pump charge carriers to the terminals). Some students may say that physicists got it wrong because we now know that electrons flow the other way. Whilst there would have been some advantages in reversing the definition of current flow (or of sign of charge on an electron) it is really an arbitrary choice. You can illustrate this by discussing current flow and movement of charge carriers in an electrolyte (or an ionised gas). Positive ions go one way, negative ions go the other way, and so however current is defined there will always be examples where current direction and charge carrier movement are opposite.

Current flows all around a circuit

Including through the cell itself.

They will find it hard to believe that charge carriers on average drift slowly and yet the effects of an electric current are transmitted very rapidly (at the speed of light in the medium). It may be worth pointing out that the electrical influence is spread through the field between charges and this travels at the speed of light. At a lower level the analogy of cars moving off when a traffic light changes is good – the influence spreads down the line of cars far more rapidly than the speed of any individual vehicle.

A useful analogy for charge flow – a bicycle chain

The chain is a way of doing work remotely. It allows a cyclist to pedal in one place in order to turn a wheel in another place. Having cycled for ten minutes, the energy stored chemically by the cyclist (the cell) will have gone down. The rate at which links pass any point is constant all round the circuit

i.e. the flow of links (the current) is not used up. Also, the chain itself is not used up (neither is charge) and stops when the cyclist stops pedalling (when the circuit is switched off). The quantity that is 'used up' is the reactants (sugars plus oxygen) in the cyclist (the chemicals in the cell).

Yet another analogy

Skiers (charges) being lifted up a mountain by a ski lift (working mechnically or electrically) and then skiing down a slope (resistor). This is particularly useful for the idea of voltages in parallel circuits. Parallel slopes drop different skiers through the same vertical height (equal voltages across components in parallel).