Capacitors & Charge
Circuits   electronics   resistors   capacitors

voltage on a cap, charging
v = v₀[1–e^(–t/τ)]
v₀ is the battery voltage
v is the voltage after time t
R is resistance in ohms,
C is capacitance in farads
t is time in seconds
RC = τ = time constant
After 1τ, v = 0.63v₀
After 2τ, v = 0.86v₀
After 3τ, v = 0.95v₀
After 5τ, v = 0.993v₀

current into a cap, charging
v = v₀[1–e^(–t/τ)]
v₀ is the battery voltage
i is the current after time t
R is resistance in ohms,
C is capacitance in farads
t is time in seconds
RC = τ = time constant
i = (v₀/R)[–e^(–t/τ)]

voltage on a cap, discharging
v = v₀e^(–t/τ)
v₀ is the initial voltage on the cap
v is the voltage after time t
R is resistance in ohms,
C is capacitance in farads
t is time in seconds
RC = τ = time constant
After 1τ, v = 0.37v₀
After 2τ, v = 0.14v₀
After 3τ, v = 0.05v₀
After 5τ, v = 0.807v₀

Current in an inductor
Iʟ = (V₀/R)(1–e^(-t/τ))
V₀/R = I₀, steady state current

Voltage across inductor
Vʟ = V₀e^(-t/τ)
Vʟ is the voltage after time t
V₀ is the  battery voltage
R is resistance in ohms
L is inductance in henries
t is time in seconds
L/R = τ = time constant

Parallel plate cap 
C = ε₀εᵣ(A/d) in Farads
   ε₀ is vacuum permittivity, 8.854e-12 F/m
   εᵣ is dielectric constant or relative permittivity
    of the material (vacuum = 1)
   A and d are area of plate in m² and separation in m
or C = ε₀εᵣ(A/d) in pF, ε₀ is 8.854

Capacitance/unit length of a long cylinder is
   C/L = (2πεᵣε₀) / (ln (b/a))
   b is radius of outside conductor
   a is radius if inside conductor
   εᵣ is dielectric constant (vacuum = 1)
   ε₀ is 8.8542e-12 F/m

Capacitance of a sphere is
   C = 4πε₀εᵣR
   εᵣ is dielectric constant (vacuum = 1)
   ε₀ is 8.8542e-12 F/m
   R is radius in meters

Energy in a Capacitor in Joules
E = ½CV² = ½QV = ½Q²/C
Q = CV
Q is charge in coulombs
C is capacitance in Farads
V is voltage in volts
E is energy in Joules

V = Energy / charge

Capacitor markings

Most capacitors have numbers printed on their bodies to
indicate their electrical characteristics. Larger
capacitors like electrolytics usually display the
actual capacitance together with the unit (for example,
220 μF). Smaller capacitors like ceramics, however, use
a shorthand consisting of three numbers and a letter,
where the numbers show the capacitance in pF
(calculated as XY × 10Z for the numbers XYZ) and the
letter indicates the tolerance (J, K or M for ±5%, ±10%
and ±20% respectively).

Additionally, the capacitor may show its working
voltage, temperature and other relevant
characteristics.

A capacitor with the text 473K 330V on its body has a
capacitance of 47 × 103 pF = 47 nF (±10%) with a
working voltage of 330 V.

relative permittivity
 or dielectric constant εᵣ
Vacuum 1 (by definition)
Air 1.000590
PTFE/Teflon 2.1
Polyethylene 2.25
Polyimide 3.4
Polypropylene 2.2–2.36
Polystyrene 2.4–2.7
Carbon disulfide 2.6
Paper 3.85
Electroactive polymers 2–12
Silicon dioxide 3.9 [3]
Concrete 4.5
Pyrex (Glass) 4.7 (3.7–10)
Rubber 7
Diamond 5.5–10
Salt 3–15
Graphite 10–15
Silicon 11.68
Ammonia 26, 22, 20, 17
(−80, −40, 0, 20 °C)
Methanol 30
Ethylene Glycol 37
Furfural 42.0
Glycerol 41.2, 47, 42.5
(0, 20, 25 °C)
Water 0º 88
Water 20º 80.1
Water 100º 55.3
Water 200º 34.5
Hydrofluoric acid 83.6 (0 °C)
Formamide 84.0 (20 °C)
Sulfuric acid 84–100 (20–25 °C)
Hydrogen peroxide 128 aq–60 (−30–25 °C)
Hydrocyanic acid 158.0–2.3 (0–21 °C)
Titanium dioxide 86–173
Strontium titanate 310
Barium strontium titanate 500
Barium titanate 1250–10,000 (20–120 °C)
Lead zirconate titanate 500–6000
Conjugated polymers 1.8-6 up to 100,000
Calcium copper titanate >250,000