dielectrics ph 203 professor lee carkner lecture 9
TRANSCRIPT
Dielectrics
PH 203
Professor Lee Carkner
Lecture 9
Test 1 on Monday Covers the whole course through today
Chapters 21-25 10 multiple choice (20 points) 4 problems (20 points each) Equations and constants given
but not labeled Bring calculator
No PDA’s, no cellphones, no sharing Study
PAL’s Notes Homework
Other Capacitors
We can find C by solving V = ∫ E ds for a path between the plates
If we do this we find: Capacitance only depends on the geometry
of the plate arrangement (and
Cylinder
For a capacitor made from two coaxial cylinders, the area is 2rL and thus E = q/(20rL)
Integrating yields:
C = (20)[L / ln (b/a)] Where “ln” is the natural log, a is
the radius of the inner cylinder and b is the radius of the outer
Sphere For a capacitor made from
two concentric spherical shells, the area is 4r2 and thus E = kq/r2
C = (40)[ab/(b-a)]
Note for a single sphere:
Where R is the sphere radius
Between the Plates
In our treatment of the capacitor we assumed the space between the plates was filled with air
Each material has a dielectric constant, , that is multiplicative factor in the capacitance
C = 0A/d
Dielectric
The polarized material partially cancels out the electric field between the plates reducing the voltage
A dielectric allows a capacitor to store more charge with the same voltage
Dielectric Constant The dielectric constant is always greater than one
It is the number of times greater the capacitance is
compared to the air filled case
e.g. if we add a capacitor with = 2 we double the capacitance and the charge stored for a given voltage
Prevents “shorting out”
Breakdown The dielectric must be an insulator
If the voltage is large enough, the charge will jump across anyway
While Q = CV, there is a limit to how much we can increase Q by increasing V
When the voltage is too high and the capacitor shorts through the dielectric, it is called breakdown
Dielectric Strength
The field between the plates however depends on the voltage applied and the plate separation, d
E = V/d
Decrease the voltage Increase the plate separation
Energy in a Capacitor
Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch
Charge stops moving when the V across the plates is equal to the V of the battery
Charging a Capacitor
Total Energy
Energy = 1/2 Q V =1/2 C (V)2 = Q2/2C since Q = C V
Large C and large V produce large stored energy
Next Time
Test #1 For next Wednesday
Read 26.1-26.3 Problems: Ch 26, P: 1, 6, 13, 15
Three identical capacitors are connected in parallel. If a total charge Q flows from the battery, what is the charge on each capacitor?
A) Q/3
B) Q
C) 3Q
D) 6Q
E) 9Q
Consider two capacitors in series with a battery, two capacitors in parallel with a battery and a lone capacitor connected directly to a battery. If all the capacitors and batteries are identical, which ranks the situations from most to least charge stored?
A) Series, lone, parallel
B) Parallel, series, lone
C) Lone, series, parallel
D) Parallel, lone, series
E) Series, parallel, lone
If two capacitors are in series and a third capacitor is added in series, what happens to the total charge stored?
A) It goes up
B) It goes down
C) It stays the same
D) It depends on the C value of the new capacitor
E) It depends on the voltage of the battery