Conductors, Capacitors and Dielectrics

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AP Physics - Core Concept Cheat Sheet
15: Conductors, Capacitors and Dielectrics
Key Physics Terms
• Charge: A fundamental intrinsic property of matter that
gives rise to the attractions and repulsions between
electrons and protons.
• Electron: A small, light negative particle. Electrons orbit
around the nucleus of the atom.
• Polarized: Separation or alignment of the charges in a
neutral body so that like charges are grouped together,
resulting in a positive and a negative region.
• Electric Field: A force field that fills the space near any
charge.
• Electric Field Line: A representation of a field using a line
whose direction is that of the force that a tiny positive
charge would experience if placed in that field. Field lines
always start at positive charge and end on negative charge.
• Electric Potential Difference: The work done to move a
1 Coulomb charge between two points in an electric field.
Measured in Volts and sometimes called Voltage.
• Conductor: Material where electrons are loosely bound
and are able to flow throughout, current flows due to the
free electrons.
• Insulator: Materials where electrons are bound and
current does not flow easily.
• Semiconductor: Materials whose electrical properties are
in between insulator and conductor.
• Superconductor: A material where electrons flow without
any resistance. Generally, superconductivity only occurs at
very low temperatures.
• Resistor: Devices used to control or regulate the amount
of electric charge flowing.
• Resistivity: An intrinsic property of a material that
partially determines the resistance of a wire.
• Capacitor: A device used to store or accumulate electric
energy. This is done by oppositely charging two nearby
conductive surfaces that are not in contact with each other.
• Dielectric: An insulating material that may be inserted
between the plates of a capacitor to increase charge
storage capability.
• Dielectric Constant: The factor that describes the
additional capacitance gained by adding a dielectric
material between the plates of a capacitor.
Variables Used
• L = Length
• A = Area
• ρ= resistivity
• R=resistance, electrical
• q = charge
• E = electric field
• d = distance
• V = Voltage
• C = Capacitance
• εo = permittivity of free space
• K = dielectric constant
• PE = potential energy
• Uc = energy stored in a capacitor
Typical Key Metric Units
• Distance or length: meters, m
• Area: squared meters, m2
• Charge: Coulombs, C
• Capacitance, Farads, F (1F =1 C/V=1 C2
/N•m= 1 J/V2
)
• Energy or work: Joules, J
• Voltage : Volts, V (1 V =1 N•m/C=1 J/C)
• Electric Field: N/C
• Resistance: Ohms, Ω
• Resistivity: Ohm meters, Ω•m
• Dielectric constant: no units, simply a ratio
Key Constants
• εo = 8.85 x 10-12
C2
/N•m2
• 1 C = 6.25x1018
electrons
• Charge on an electron = -1.6 x 10-19
C
Key Formulas
•
L
R
A
ρ
=
• q=CV
• o
Kε A
C =
d
•
2
c
1 1
U CV qV
2 2
= =
•
PE
V Ed
q
= =
Factors that Determine Resistance of a Wire
• Resistivity of wire material
• Length of wire
• Cross sectional area of wire
• Temperature of wire
Problem Solving Tips
These tips will make it easier to solve any physics problems.
• Thoroughly read the entire problem.
• Draw a diagram if needed.
• Identify all given information.
• Identify the quantity to be found.
• Select appropriate formula(s) that incorporate what you
know and what you want to find.
• Convert units if needed. Capacitance and charge units
often need to be converted. Keep track of units during
calculations.
• Do any mathematical calculations carefully.
Capacitor Diagram
Typical Capacitance Problem
Example: A 300 μF parallel plate capacitor has plates, 1.0
x10-6
m apart. The gap contains a material with a dielectric
constant of 4.5. Find the area of each plate for this situation?
Begin with the capacitance formula. o
Kε A
C =
d
Rearrange to solve for the unknown area.
0
Cd
A =
Kε
Substitute values, converting the microfarads into Farads.
Remember that 1 F = 1 C2
/N•m
6
410 F
300 μF x 3.00 x 10 F
1 μF
−
−
=
-4 2 -6
2
-12 2 2
(3.00 x 10 C /N•m)(1.0 x 10 m)
A = = 7.5 m
4.5 (8.85 x 10 C /N•m )
Units and sig fig are correct. Magnitude is reasonable.
How to Use This Cheat Sheet: These are the keys related this topic. Try to read through it carefully twice then recite it out on a
blank sheet of paper. Review it again before the exams.
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Dielectric
Here is a typical diagram of a
parallel plate capacitor. Note the
equal and opposite charges on the
plates. The material between the
plates is the dielectric. It’s used
to increase the capacitance. The
circles in the dielectric represent
the individual molecules that are
polarized.