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Formula Sheets / Physics

Chapter 19

Capacitance

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Capacitors Combinations Dielectrics Energy stored

Capacitors

$C = \frac{Q}{V};$ parallel plate $C = \frac{ε _{0} A}{d};$ sphere $C = 4 π ε_{0} R$
Spherical and cylindrical
$C = 4 π ε_{0} \frac{ab}{b - a},$ $C = \frac{2 π ε _{0} L}{ln ( b / a )}$

Combinations

series: $\frac{1}{C} = \frac{1}{C _{1}} + \frac{1}{C _{2}} + \dots;$ parallel: $C = C_{1} + C_{2} + \dots$
Charging (RC)
$q = C V (1 - e^{- t / R C}),$ discharging: $q = q_{0} e^{- t / R C},$ $τ = R C$

Dielectrics

$C = K \frac{ε _{0} A}{d};$ slab of thickness $t : C = \frac{ε _{0} A}{d - t + t / K}$
Conducting slab
$C = \frac{ε _{0} A}{d - t}$

Energy stored

$U = \frac{1}{2} C V^{2} = \frac{Q ^{2}}{2 C} = \frac{1}{2} Q V,$ $u = \frac{1}{2} ε_{0} E^{2}$
Sharing charge
$Δ U = \frac{C _{1} C _{2} ( V _{1} - V _{2} ) ^{2}}{2 ( C _{1} + C _{2} )}$ lost
Force between plates
$F = \frac{Q ^{2}}{2 ε _{0} A}$

Electrostatics Current Electricity