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3.1.5.
Capacitance <CJ chap 19..5-19.7 >
3.1.5.1.
Discussion
3.1.5.1.1.
Given
any two neutral conductors that are separated, say A and B, then carry a charge Q from A to B
3.1.5.1.1.1.
A potential difference of V volts
between A and B will result from this action.
3.1.5.1.1.2.
If 2Q, 3Q etc is moved from A to B
then 2V, 3V etc will be the resulting voltage difference.
3.1.5.1.1.3.
This constant ratio of Q/V depends
upon the geometry and is defined as the capacitance C =Q/V
3.1.5.1.2.
Capacitors
were the earliest methods of storing charge, voltage, and electrical energy.
3.1.5.1.3.
The
unit of capacitance is the Farad (F) = Coulomb/Volt (Q/V)
3.1.5.2.
Mathematical
3.1.5.2.1.
C = Q / V <Farad (F) = Coulomb / Volt >
3.1.5.2.2.
Of a
parallel plate capacitor C = q/V = sA / (Ed) = sA / ((s/e0)d) or C = e0 A/d
3.1.5.2.3.
Combinations
of capacitors:
3.1.5.2.3.1.
In parallel Ctotal = C1 + C2 + …. Cn
3.1.5.2.3.2.
In series 1/Ctotal = 1/C1 + 1/C2 + …. 1/Cn
3.1.5.2.4.
Energy
stored in a capacitor W = ½ Q V = ½ C V2
3.1.5.2.5.
Dielectric
material
3.1.5.2.5.1.
If a dielectric material is
placed in a capacitor then V=V0 /k
3.1.5.2.5.2.
Where k = dielectric constant k =
1 for vacuum or air, 3.7 paper, 80 water…
3.1.5.2.5.3.
It follows that C = k C0
3.1.5.3.
Advanced
3.1.5.3.1.
Capacitance
values for simple geometries:
3.1.5.3.1.1.
A charged sphere of radius R: C = 4peo R
3.1.5.3.1.2.
Parallel plates of area A and
separation d : C = eo A /d
3.1.5.3.1.3.
Cylindrical capacitor of length l
and inner & outer radii a & b : C = l / [2 k ln (b/a)]
3.1.5.3.1.4.
Spherical capacitor of inner and
outer radii a & b: C = ab /[k (b-a)]