Physicopoeia

φυσικοποιΐα
THINGS I WISH I'D KNOWN WHEN I STARTED TEACHING PHYSICS

HOW TO BE A RESISTOR JEDI

Estimating an answer to a question before you reach for the algebra or your calculator is always a good idea to avoid silly mistakes. The parallel resistor formula is well-known for its ability to trip people up:

 


The classic pupil mistake is to get so bogged down inverting all the resistor values on the right-hand side of the equation that they forget to invert the final answer. So, if you had a 75Ω, a 100Ω and a 50Ω resistor all connected in parallel, this mistake would give you the rather ridiculously tiny answer of 43 milliOhms, but many pupils won't realise how unrealistic this is.

 

The ability to just look at a parallel combination of resistors and say 'OK, the total resistance is going to be about [whatever] Ω' is wonderfully useful: it makes silly mistakes with the formula less likely, it strengthens your understanding of electric circuits and, to quote Obi-Wan Kenobi, it 'can have a strong influence on the weak-minded'.

For example, if you had a 75Ω, a 1kΩ and a 50kΩ resistor all connected in parallel, you can instantly say that the total resistance will be a bit less than 75Ω and, since the other two resistors are quite large, it'll probably be around 70-ish Ohms. Using the formula gives... 69.7Ω. (Thank you, ladies and gentlemen; I'm also available for children's parties, weddings and bar mitzvahs)

If you or your pupils want a bit of training on how to do this, and why it works, here's a sheet I wrote: