GeekDad Puzzle of the Week – Capacitor Combinatorics

Geek Culture

Looking back to my Physics coursework, one of the most interesting (and challenging) aspects was calculating the overall capacitance of a set of capacitors. As you may recall, capacitors in parallel sum the capacitance of each element; in series, they are the inverse of the sum of the inverses of each element.

Put graphically:

Capacitors in Parallel: Capacitors in Series:
cap_parallel cap_series2
60 µF + 60 µF = 120 µF 1/(1/60 µF + 1/60 µF) = 30 µF

There’s only one way to “wire in” a single 60 µF capacitor, and three different ways to wire in up to two 60 µF capacitors – one by itself, two in series, and two in parallel.

This week’s GeekDad Puzzle of the Week is to determine how many different capacitance values can be created by wiring together up to 10 identical 60 µF capacitors. Note that not all 10 need to be used for each circuit, and that subsets can be used in parallel and in series to each other.

Please submit your answers to GeekDad Central for your chance at this week’s $50 Gift Certificate from ThinkGeek. Good luck, and happy puzzling!

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