Electricity 1 — DC Circuits

Capacitors — charging up

continues from lesson 4 — values defined earlier in the course stay live here

A capacitor is a small bucket for charge. Through a resistor it fills not linearly but exponentially: fast at first, ever slower. The time constant τ = R·C sets the pace — after one τ it is 63% full, after five, full for any practical purpose.

C_{1} := 100e-6 F

= 0.0001 F capacitance (100 µF)

\tau = R_{1} \cdot C_{1}

= 0.006 ohm F time constant

\tau_{n} = 0.006

the same τ as a plain number (s), for the plot

12 * (1 - exp(-x / tau_n))

capacitor voltage while charging toward 12 V (x in seconds)

Where next: the Σ library has RC time constant, wire resistance, AWG gauge and voltage-drop formulas — the bridge from circuit theory to real wiring.