Scholarship physics: When the obvious is not-so-obvious

On Tuesday my physics skills were put under the spotlight. Back in November, I think, I was discussing with Sam Hight from the Physics Lounge  ( ways that we could, together help high-school students in their physics. One of the things we came up with is that I had a go at doing the 2012 Scholarship Physics Paper, live. In other words, I’d get filmed attempting the paper – under pseudo-exam conditions – specificially, I wouldn’t have seen the questions before -I’d be going straight into it.

The idea here was to give the students a realistic view of problem solving and how an experienced physicist (if I may be so bold as to call myself that) reasons and decides what’s important and what isn’t. Too often when model answers are presented to a problem one is left wondering: "That’s all very well, but HOW do I know I should approach the problem that way?", or "HOW do I know that such-and-such bit of physics is what is relevant and will get me to the end point before I start?" With hindsight and enough time, most answers to exam questions can be condensed down into something really neat and snappy (the model answers!), but the reality is that hindsight doesn’t occur until a couple of days AFTER the exam when it isn’t much use.

So Sam filmed me going through the paper. We had a few teething problems with the camera equipment, which meant we only got through four of the six questions, but hopefully we’ll get the other two filmed soon. (Of course, I’ve seen the questions for these other two so it won’t be quite as authentic.) Sam will work on the videos and hopefully they’ll appear on Physics Lounge before too long. I hope they are useful. If students hadn’t worked it out already, these questions are tough, and they take a bit of thinking about.

So, if you dare, turn with me to question 5, part (b) on the paper.  I wonder sometimes just how the examiners dream up some of these questions. In this question, twelve electrical cells (commonly called batteries), each of 1 volt  are connected in a loop. That’s it – no other electrical components. This question should have carried a warning "Don’t try this at home!" So, if a voltmeter is placed across three of these cells, what voltage does it read?

Well, you will see the embarrassing shambles I made of it on the movie, when it gets posted. But I got there in the end, and Sam and I had a good discussion on it that’s captured on the movie. In fact, the more I think about it, the more blindingly obvious it is. It really is just such a simple argument. By symmetry (a powerful tool in physics), each cell must have the same potential difference across it. Call it V.  If we move one terminal of the voltmeter all the way around the loop, adding one cell at a time, the potential must increase by V each step, so a total of 12 times V. However, after going around in a loop, we get back to where we start, so the potential cannot have changed. So 12 times V must be zero, and V must be zero.

In other words, there is no voltage over a short-circuited battery. Which is obvious – it’s a short-circuit -by definition they are at the same voltage.  Obvious in hindsight, that is.







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