Resistors in series add; in parallel the net is a little less than the smaller one

This is Collins’ ‘Ohm’s Law for Dummies’ (Rule #13), the minimum electronics needed for practical circuit hacking. Two resistors end-to-end (series) add: 10 kΩ + 10 kΩ = 20 kΩ. Two resistors joined at both ends (parallel) give a net of 1/(1/R1 + 1/R2), which is always a little less than the smaller of the two (two 10 kΩ in parallel = 5 kΩ). The practical consequences for a hacker who understands that skin is a resistor: touching a circuit adds finger resistance in parallel with the timing resistor, lowering net resistance and raising clock pitch; wiring a pot in series with the resistor only raises total resistance (slows/lowers pitch); replacing the resistor entirely with a larger pot gives control in both directions. The same series/parallel logic governs filter tone controls and mixer summing networks. Capacitors resist current in a frequency-dependent way and combine with resistors to set RC-oscillator frequency.

Examples

Flesh (~1 MΩ) in parallel with a 100 kΩ clock resistor → net ~91 kΩ, pitch up ~10%. A 1 MΩ pot in series with the 100 kΩ resistor → ~1.1 MΩ total, extending the range downward. Two 10 kΩ in parallel → 5 kΩ.

Assessment

A toy’s clock circuit has a 220 kΩ timing resistor and a wet finger across it raises the pitch — explain why using the series/parallel rule. For a 200 kΩ timing resistor, explain whether a 1 MΩ pot in series or in parallel allows the lowest frequency, and how you would make the pitch fall below stock.