Level 2-3 Notes On Capacitance

Forces and Fields

diagram showing two oposite charged particles and electric field lines

Diagram of two electrically charged bodies.

The force of attraction or repulsion between two electrically charged bodies is proportional to the magnitude of their charges and inversely proportional to the square of the distance between them.

Force is proportional to q1q2/d2 = force= kq1q2/d2 where k=9*109 this is coulombs law. Whenever a p.d. is established between two points, an electric field will always exists.

When a charged body is placed next to an uncharged body, an induced charge of opposite sign appears on the surface of the uncharged body. This is because lines of force terminate on the uncharged body.

Electrical field strength is given by E= V/d it is also called the potential gradient. This equation is applied to the electrical field between two parallel plates.

Fringing is where the field deviates from straight lines. It reduces field strength. For this equation fringing is thought to be minimal.

6.4 Capacitance Definition

simplified capacitor diagram

The presence of a static electrical field indicates the presence of equal and opposite positive and negative charges on two plates.

The property of these two plates that determines how much charge corresponds to a given p.d. is called the capacitance.

The unit of capacitance is called the farad and is usually measured in Micro Farads( )

6.5 Capacitors

symbol for a capacitor

capacitor symbol

Capacitors are simply defined as two plates separated by a dielectric. The charge stored in capacitor is given by Q=I*t where: Q = charge, I = current and t= time in seconds.

6.6 Electric Flux Density

Unit flux is defined as emanating from a point with charge 1 coulomb the unit for flux is the Coulomb but because it is flux it has a different symbol.

Electric flux density is the amount of flux that is passing through an area (call it A) that is perpendicular to the direction of the flux. The electric flux density is given by D= Q/A

Relative and Absolute Permitivity

6.7 The Flux density divided by field strength is a constant for any region within an electric field.

D/E = 0 r

Where r is the relative permitivity and 0 is the permittivity of free space.

r has no units it varies from material to material.

0 rand is called the absolute permitivity.

D=Q/A.

6.8 Parallel Plate Capacitor

interleaved capacitor

For a parallel plate capacitor another way to increase capacitance is to interleave the plates.

The capacitance (C) of such a capacitor is given by:

C= 0 rA(n-1) /d

Where n is the number of plates, A is the area of the plates, d is the separation and C is the capacitance.

6.9 Capacitors Connected in Parallel

Ctotal=C1+C2+C3 for three capacitor

Qtotal=Q1+Q2+Q2

Some Related Equations

Q=CV

CV=C1V1+C2V2+C3V3

V1=V2=V2

Capacitors Connected In Series

3 capacitors in a series circuits

The Q charge on C1 induces a+Q charge on C2 therefore the charge must be the same on all capacitors in series the voltage depends on the capacitance and sums up to V.

Given that V=Q/C then V=Q/C1+Q/C2+Q/C3

1/C=1/C1+1/C2+1/C3 1/Cn

For two capacitors connected in series

Ctotal=C1*C2/(C1+C2)

Dielectric Strength

The dielectric strength is the maximum field strength the dielectric can withstand, it is given by

Dielectric Strength Em=Vm/d

Energy Stored in a capacitor=Joules in a capacitor=W=(1/2)CV2