ELECTRICITY

V = IR, and the power VI = I²R = V²/R — three routes to the same watt, all of it heat. Series adds, parallel divides, and R_series × R_parallel = R₁R₂ to the bit.

Q = CV; the energy ½CV² is the triangle under the Q–V line. And the mirror of resistors — caps in parallel ADD, in series reciprocate, with C_series × C_parallel = C₁C₂.

RC·dV/dt + V = 0 at every frame — the exponential goodbye, audited.

A perfect ratio machine — until you connect the thing you built it for.

Lq″ + Rq′ + q/C = 0 — the damped oscillator’s own code, running in copper.