Science Puzzle by M. Deal

Electricity Cable Here is an electricity extension cable. There is nothing unusual about it but it has a curious label and warning.

Can it have a current of 10 A going through it when it is uncoiled or coiled? When it is coiled what is the maximum current that can pass through the lead? It is the same lead whether it is coiled or uncoiled so why is there a difference in the current that can be carried? Power (W) = Voltage (V) x Current (A) Power = Voltage x Current So Current = Power ÷ Voltage Current = 960W ÷ 240V = 4A What do these warnings mean? It shows how much power can be provided to appliances connected to the extension lead when it is coiled and uncoiled. So the lead can take the greatest current (10A) when it is uncoiled. 2400W = 240V x Current Hint SolutionEnd presentation

Hints Here are a few hints with increasing helpfulness. You can jump back to the previous slide at any point by using the ‘return button’. Hint 1: On a shorter 5m extension lead it carries the same sort of warning. The lead can carry a 4A current when coiled and a 5A current when uncoiled. Length of cable is a factor. Why should this be? This is the last hint. Please select from the three buttons on this screen in order to move onto the next slide. Hint 2: Can you think of any other wires in which the current is kept low? What was the reason for this? SolutionEnd presentation

Solution Electric currents have a heating effect and the larger the current, the larger this heating effect is. Appliances that get hot (kettles, electric fires, toasters, etc) need a large current and therefore have a high power rating. When the lead is unwound the heat can escape from all the large surface area. When the cable is used but is wound up then the cable heats itself up and is also encased so heat builds up and cannot easily escape. This heat can be enough to melt the insulation, possibly starting a fire. In what way would you expect the warning labels to differ for shorter or longer extension leads? 25m lead 10m lead

The longer the lead, the greater the possible heating effect and therefore the greater the difference between the currents allowed when the lead is coiled and uncoiled. This 25 metre extension lead can deliver:  7 20W of power (at 240V) when coiled  3 120W of power (at 240V) when uncoiled = 3A = 13A What is the maximum current that it can take each time? This 10 metre extension lead can deliver:  9 60W of power (at 240V) when coiled  1 200W of power (at 240V) when uncoiled = 4A = 5A What is the maximum current that it can take each time? There is a difference between the two leads for the current they can take when unwound because the leads are of different thicknesses. Leads have to be thicker to carry larger currents. End presentation

Extra information It is not always so easy to work out the power being drawn through an extension cable. If more than one socket is used then the power being drawn through each socket must be added to find the total power. Some extension leads and power packs are fitted with a thermal cut out. The button ‘clicks out’ and the circuit is broken if a high current flows. These can use the heating effect of too large a current to bend a bimetallic strip and break the circuit. A 60W light bulb, a 30W Video player and a 100W television are all connected into an extension lead. If mains electricity is 230V find the: power drawn through the extension lead current flowing through the extension lead 60W + 30W + 100W = 190W I = P ÷ V = 190W ÷ 230V = 0.83A

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