Capacitors

change in V = Q / C

C = Q / change in V

C = BoA / D (B is the replacement for the greek constant)

C = K Bo A / D (dielectrics) (B is the replacement for the greek constant)

Uc = ½ C change in V ²

Uc = ½ Q change in V

Uc = Q² / 2C

Time constant = RC 

Battery does work to separate the charges, which will increase potential energy stored in electric field

Dielectrics

increase capacitance and potential energy

organize the atoms and align the opposite charges to each other

decrease electric field

With a capacitor and change in V is same

when C increases Q increases

when C decreases Q decreases

No capacitor Q is the same

C increases change in V decreases

C decreases change in V increases

Work done on 1st charge is 0

parallel has less equivalent resistance  

Charging/Discharging

charging time is proportional to capacitance and resistence 

discharging is exponential decay using the equations

I = Io e^(-t/time constant)

change in V = change in V initial e^(-t/time constant)

Parallel

charge is added together 

Qt = Q1 + Q2

Capacitors have same voltage 

Vt=V1=V2

plugging in CV for Q we can derive the equation for capacitors 

Ct = C1 + C2

capacitance is added together

Series

charge in capacitors are equal 

Qt = Q1 = Q2

potential is added 

Vt = V1 + V2

plugging in CV for Q we can derive equation for capacitors 

1/Ct = 1/C1 + 1/C2