Circuits Part 4: Capacitor Networks & Bioelectricity

Capacitor Networks and RC Circuits

Capacitors combine opposite to resistors: directly in parallel, reciprocally in series. An uncharged capacitor acts like a wire the instant a switch closes and like a break once charged. The time constant $\tau = RC$ sets the pace: about 63% after one $\tau$, essentially done after about $5\tau$.

Bioelectricity

The cell membrane is a capacitor (the bilayer) in parallel with resistors (the ion channels). Myelin lowers membrane capacitance and raises membrane resistance, speeding conduction. A defibrillator charges a capacitor slowly and releases its energy in a brief pulse.

Key Takeaways

• Capacitor combination rules are the reverse of resistor rules.
• Steady state: no current through a capacitor branch.