THE MAXIMUM POWER THEOREM
Once you've taught about EMF and Internal Resistance, most A-level syllabuses don't expect pupils to be taught much else that they haven't already come across in previous years. Your good candidates may then start to get a bit bored with the topic. Here's a nice bit of extension work that takes the ideas of EMF and internal resistance and pushes them a little further. This sheet takes a calculus-based approach:
Whereas this Excel file shows exactly the same Physics, but takes a graphical approach instead, which can help pupils who are less mathematical. You could easily strip the formulas out of this and set it as a homework task:
For even more extension, you can show that inelastic collisions actually behave mathematically in the same way, which is quite spooky. I wrote this up for a paper a few years ago:
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Almost immediately, it pleased me greatly that someone else realised that the result was of even more general applicability:
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Atkin K (2013). Energy transfer and a recurring mathematical function. Physics Education 48(5)
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