CHARGE CONSERVATION

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.

N(k·t½) === N₀/2ᵏ bitwise — the law of halves as an identity, no dice anywhere.

At the daughter’s peak, inflow === outflow to the bit — and the ledger closes at every instant.

t = t½·log₂(N₀/N) — a quarter left is 11,460 years, exactly, and the round trip is bitwise.

T = 2πm/qB — no speed in it: five radii, one period, audited to 1e-15. The spiral obeys √k to the bit.

m = qBr/v — mass from a photograph: the roundtrip returns carbon-12 bitwise.

Crossed E⊥B pass exactly one speed: v = E/B, with no q and no m in the verdict.

ε = BLv, and the ledger: Fv === I²R with residual 0 at every speed — work becomes heat, joule for joule.

Exact finite-field overlap drives Φ, ε, the full RL transient, signed magnetic force, and Wext = QR + UL on one clock.

B = μ₀nI and F/L = μ₀I²/2πd — the old ampere audited to one ulp.

At ω₀ the reactances cancel BITWISE and φ === 0 — driven Q equals free-ringing Q, one number.

V₁I₁ === V₂I₂ — the invoice, bitwise across the whole plane at 2:1. Volts down, amps up, never free.

Two charges: the field vanishes at x = r/(1+√(q₂/q₁)) — but ∇²V=0 makes it a saddle, so nothing rests there. Earnshaw, drawn.

A sideways voltage V_H = IB/nqt — and its SIGN names the carrier. Electrons and holes bend the same way but flip the voltage.