Tuesday 24 November 2009

Which Circuit Runs a Battery Down Quickest?


Imagine three circuits.

1. One bulb.
2. Two bulbs in series.
3. Two bulbs in parallel.

The batteries are the same in each circuit. In what order do the batteries run down? (If it matters to you, assume that the batteries all have negligible internal resistance and that the resistance of the bulbs doesn't change with current).

This is the correct order

Circuit 3 (parallel) runs down after, say 1 hr
Circuit 1 (single) runs down after 2 hours
Circuit 2 (series) runs down after 4 hours

The times assume (incorrectly) that the batteries provide a constant voltage before suddenly dropping to zero.

Remember that each of the parallel bulbs are as bright as the single bulb. So the two bulbs in parallel demand energy from the battery twice as quickly as one alone. That’s why the parallel circuit runs down first.

It might be tempting to believe that the series circuit runs down at the same time as the single bulb. This would assume that each series bulb was half as bright as one alone. But in fact each of the series bulbs is a quarter as bright. Brightness depends on how quickly energy is transferred, in other words, power.

Power depends on both current (how quickly charges are arriving) and voltage (how much energy each charge transfers). In the series circuit the current round the circuit is halved and the voltage is shared between two bulbs, so energy is transferred to each bulb only a quarter as quickly as if it were by itself.

In this simulation you can drag a power meter to different parts of a series and parallel circuit to see how the different brightnesses can be explained.

5 comments:

  1. Hi Julian, I am a physics teacher and I just found the Furry Elephant site. I felt a bit odd subscribing when there were only two topics covered (electricity and radiation) so I googled to see what I could find out about your site. You had said that Forces were coming, but I didn't know whether that had been said three years ago or whatever, and that the Forces may never actually be coming. I absolutely love what you've created and I'd love to use it. I was pleased to find this recent blog so I presume you are still working on updating or adding to the furry elephant site. You can contact me at alvktt@optusnet.com.au if you don't want to post an answer here. All the best, Amanda Thompson

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  2. Hi Julian. Stumbled across your site whilst trying to find information for my son who is only in year 2 but is learning about electricity already at school. I think it is fantastic and it really appealed to my son. I am going to try and persuade my son's primary school to subscribe - do you sell to primary schools? Thanks, Science Mummy

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  3. Hi Amanda, Thanks for the contribution. I've been doing some work on forces but I've also been spending a lot of time on the website side of things. I'm pretty sure I won't have any completely new content within the next twelve months, or at least not packaged up as lessons, though I may be able to release some activities on a more ad hoc basis.

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  4. Hi Science Mummy. Quite a few primary schools do use Furry Elephant, particularly if there's a lack of specialist science knowledge within the school. At the moment our individual subscriptions can actually be used by the whole school. So your primary school could subscribe as an individual for just GBP 4.95 a month using a credit card and unsubscribe again when they've finished the topic. Hope this helps and thanks for the support.

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  5. hey! loving the furryelephant site, makes a great substitute phys teacher (: thanks so much!
    would love it even more if you could please throw in a few more equations to summarise it all

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