Fibonacci numbers and resistor networks

Рет қаралды 470

2 ай бұрын

Exploring the relationship between the Fibonacci numbers and the effective resistances of ladder-like resistor networks, using recurrence relations.
Full derivation of nth effective resistance: • Finite resistor ladder...
And the nth term of the Fibonacci sequence (note that this starts with 1, 1 instead of 1, 2, but is easily adaptable): • nth term of the Fibona...
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#physics #mathematics #electricity #circuits #resistance #effectiveresistance #fibonacci #fibonaccinumbers #fibonaccisequence #simultaneousequations #seriescircuit #parallelcircuit #recurrencerelation #nonlinear #nthterm #voltage #current #goldenratio #reciprocal #math #science #education

Пікірлер: 7

@mingmiao364 2 ай бұрын

Perfect follow up!

@DrBenYelverton 2 ай бұрын

Thanks! I didn't spot the connection to Fibonacci numbers at first, until I started plugging values of n into the Rₙ formula from last time and noticed the pattern.

@MinMax-kc8uj 2 ай бұрын

You can put your closed form solution from the other video into that form to. Since F[2n]/F[2n-1], there is a part the cancels itself. If you put that part back in (multiplying by 1/1), your closed form should go into that.

@urgtuiop5455 2 ай бұрын

What about a 2d array of r. What would be the eqn for v at each node when driven from the extremes of a main diagonal. Can I use this to approximate the field in a conducting plate.

@DrBenYelverton 2 ай бұрын

Great question! I don't have an immediate answer and I suspect the maths involved is much more difficult, but this would definitely be interesting to investigate.