15.1. The Big Idea http://www.ck12.org
15.1 The Big Idea
When current flows through wires and resistors in a circuit as a result of a difference in electric potential, charge
does not build up significantly anywhere on its path. Capacitors are devices placed in electric circuits where charge
canbuild up. The amount of charge a capacitor can store before it “fills up” depends on its geometry and how much
electric potential is applied. The ratio of charge stored in a capacitor to the voltage applied is called itscapacitance,
measured in Farads(F). The larger the electric potential in volts, the stronger the electric field that is used to “cram”
the charge into the device. Any capacitor will fill up with enough charge and voltage. Capacitors store energy when
charged, and release it when they discharge.
Key Equations and Definitions
ε 0 = 8. 85 × 10 −^12 F/m Constant called the permittivity of free space
Q=CV Charge stored in a capacitor
U=^12 CV^2 Potential energy stored in a capacitor
C=κεd^0 A For two parallel metal plates, area A,separationd,dielectricκ
Q(t) =Q 0 e
−τt
Discharge rate of a capacitor, whereτ=RC
Q(t) =Q 0 ( 1 −e
−τt
) Charge rate of a capacitor, whereτ=RCandQ 0 =VC ̇
I(t) =I 0 e−τt
Discharge and Charge rate for current, whereτ=RCandI 0 =VR
CpNet=∑iCpi Capacitors in parallel add like resistors in series
1
CsNet=∑i1
Csi And vice versaElectric Circuit Symbol
The symbol for a capacitor is two flat plates, mimicking the geometry of a capacitor, which typically consists of two
flat plates separated by a small distance. The plates are normally wrapped around several times to form a cylindrical
shape.
MEDIA
Click image to the left for more content.