Capacitive coupling on breadboard

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FOIWATER
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I have read that between breadboard nodes there can be as much as 25 pF of capacitance.

I have a much better time understanding how parasitic induced voltages work, with respect to magnetic fields.

I have a much harder time understanding how signals can become noisy due to parasitic capacitance.

I don't understand time varying electric fields as well as magnetic fields.

Can some one help me understand how capacitance between nodes, can manifest itself as a noisy signal in said circuits?
 
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Capacitative coupling is more straightforward than magnetic coupling, imo. Just consider it as joining a capacitor of 25pF or so between the two nodes and work out the effect of this in terms of a simple (based on impedance, not just resisitance) Potential divider to find the induced voltage.

There will be layouts possible that should give a bit lower than the 25pf you quote, I think, if it's a problem but it depends upon the actual circumstance. Using an Earth plane can help a lot.