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Visual: Triangles for Calculation

Name	Resistor	Capacitor	Battery(Cell)
中文	電阻	電容	電池
Short Form	R	C	ℰ
Unit	[Ω] =[V]/[A]	[F] = [C]/[V]	[V]
Circuit Symbol
Defn(geometry/material)	ρ d/A	ε A/d	X
Relates(math)	R = ΔV / I	C = Q / ΔV	X

Circuit Elements (Symbols)	Combining Resistances

Capacitors	C = ε (A / d)	[ F ]	R & C contain material + geometry parameters
Resistors (G=R^-1)	R = ρ (d / A)	[ Ω ]
Resistors (G=R^-1)	G = σ (A / d)	[ S ]
Power	P = ΔV · I	[J/s]	P = I² R = (Δ V)²/R

R S = L S

\sum Δ V_{l o o p} = 0

Δ V_{c a p} + Δ V_{r e s} = 0

\frac{Q (t)}{C} - I (t) R = 0

\frac{Q (t)}{C} + \frac{d Q}{d t} R = 0

\to \frac{d Q}{Q (t)} = - \frac{d t}{R C} \equiv - \frac{d t}{τ}

\int \frac{d Q}{Q (t)} = - \int \frac{d t}{τ}

\ln Q (t) = - \frac{t}{τ}

Q (t) = Q (0) \exp (- t / τ)

I (t) = - \frac{d Q}{d t} = \frac{Q (0)}{τ} \exp (- t / τ) = \frac{Δ V (0)}{R} \exp (- t / τ)

Knight Chapter 28: Fundamentals of Circuits

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C G White (白愛恩), J D White (白小明)

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