/Reccurence-Resistor

Solving OPhO 2022 Recurrence Resistor Problem using code (forked from Abhiram)

Primary LanguagePython

Reccurent Resistor Networks

Extrapolating limits for Delta-Y transformation based Resistor Networks.

Question from OPhO 2022.

Screenshot 2022-07-31 at 5 08 23 PM

Method Approached

Notably, we can slowly perform Delta-Y transformations and just keep appending to a strand of resistors. Thus, we can first draw out the first Delta, which starts at a.

$$R_{strand} = \frac{R_b R_c}{\sum R}$$

We also keep alternately adding 1 ohm to each of the other resulting connections due to the 1 ohm connections.

Thus, for any resistor network of size $n$, we perform Delta-Y at $2n$ times.

Results

Loss Curve

This was the computed loss curve for $\frac{R_{eff}}{n}$.