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Review: Fill in the Table (Below)

NameResistorCapacitorBattery(Cell)
中文電阻電容電池
Short FormRC ℰ
Unit [Ω] =[V]/[A] [F] = [C]/[V] [V]
Circuit Symbol
Defn(math)ρ d/A ε A/d X
Relates R = ΔV / I C = Q / ΔV X

Key Points: DC Circuits

Electrical Symbols Illustrated Resistors

ResistersR= ρ (d / A)[ Ω ] R & C contain both physics + geometry
d and A determine how R and C add
CapacitorsC = ε (A / d)[F]
Power P = Δ V   I [J/s] P = I2 R = (Δ V)2/R

Time Constants and RC Derivation

$$ \sum \Delta V_{loop} = { Q(t) \over C } - I(t) R = { Q(t) \over C } + { dQ \over dt} R = 0 \\ \rightarrow { dQ \over Q(t)} = - { dt \over RC} \equiv - { dt \over \tau} \\ \int { dQ \over Q(t)} \, = \, - \int { dt \over \tau} \\ \ln {Q(t)} \, = \, - {t \over \tau} \\ Q(t) \, = \, \exp { \left ( - {t \over \tau} \right ) } \\ $$

Lecture Power Points: DC Circuits including RC circuits

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