1. Chapter 24 Capacitance
Capacitor is a device that stores electrostatic potential energy.
A capacitor consists of 2 spatially separated conductors which can be charged to +Q and -Q.
The capacitance is defined as the ratio of the charge on one conductor of the capacitor to the potential difference between the conductors.
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2. A d
Capacitance
Parallel Plates
Cylindrical Capacitor
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3. Question
A +Q charge is placed on a solid spherical conductor. A -Q charge is placed on a concentric conducting spherical shell.
Let V1 be the potential difference between the spheres with (a1, b).
Let V2 be the potential difference between the spheres with (a2, b).
What is the relationship between V1 and V2? a2 b +Q -Q a1
V2 < V1
(a) V1 < V2
(c) V1 > V2
(b) V1 = V2
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4. Comments on Circuit Diagrams:1 2 a b 3
Wires have no electrical resistance.
Components are ideal
PHYS241 only deals with:
Resistors, R
Capacitors, C
Inductors, L
Batteries, Generators, switches & wires
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5. Equivalent Capacitorsb Q2 Q1 C3 Q3 V C a b Q a b +Q -Q V -Q C a b +Q
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6. Capacitors in Parallel
Capacitors connected in parallel can be replaced with an equivalent capacitor that has the same total charge, Q and the same applied potential V. V C1 C2 a b Q2 Q1 C3 Q3
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7. Capacitors in Series
Capacitors are in series when a potential difference that is applied across their combination is the sum of the resulting potential differences across each capacitor. a b +Q -Q V
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8. Capacitors in Series
Capacitors that are connected in series can be replaced with an equivalent capacitor that has the same charge Q and the same total potential difference V as the actual series capacitors. a b +Q -Q V
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9. Example C1 C2 C3 a b C a b
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10. Question What is the equivalent capacitance, Ceq, of the combination?
(a) Ceq = (3/2)C
(b) Ceq = (2/3)C
(c) Ceq = 3C
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11. Question What is the relationship between V0 and V ? V0 V conductor
(Area A) +Q
(Area A)
d/3 V0 V d
conductor
d/3 -Q -Q
(a) V = (2/3)V0
(b) V = V0
(c) V = (3/2)V0
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12. Dielectrics
Empirical observation: Inserting a non-conducting material between the plates of a capacitor changes the VALUE of the capacitance.
Definition:The dielectric constant of a material is the ratio of the capacitance when filled with the dielectric to that without it.
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13. Demo: Dielectrics & Capacitance
––––––
++++
++++
––––– + + E0 k
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14. Dielectric Strength
*The maximum value of the electric field that a dielectric material can tolerate before breaking down.
* It limits the voltage that can be applied to a capacitor. The maximum voltage is called the breakdown potential.
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15. Dielectric Properties
material k
dielectric strength
(kV/mm)
air (1 atm) 3
paraffin
2.1–2.5 10
glass (Pyrex)
5.6 14
mica
5.4
10–100
polystyrene
2.55 24
H2O (200 C) 80 ?
titania ceramic
130
strontium titanate
310 8
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16. Effect of Dielectrics on the Electric Field
real charge
real charge + -
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17. Capacitors with a dielectric for Fixed Amount of Charge
For Fixed Charge, the insertion of a dielectric::
decreases the Electric Potential
decreases the Electric Field
decreases the Electric Potential Energy
The decrease in energy can be accounted for by the work done in moving the dielectric slab between the plates of the capacitor
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18. Capacitors with a dielectric connected to a battery (Constant Potential).
For a constant applied potential, the insertion of a dielectric::
increases the amount of charge on the plates
increases the Electric Field
increases the Electric Potential Energy
The increase in energy occurs because work is done to maintain the potential across the plates as the dielectric is inserted.
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19. Dielectric Combinationsk1
d/2 A k2
d/2
A/2
A/2 d k2 d k1
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20. (1) (2) (3) (A) 1 (B) 2 (C) 3 (D) None
QUIZ 9: Three circuits, each consisting of a switch and two capacitors are initially charged as indicated. After the switches have been closed, in which circuit will the charge on the capacitors remain the same?
(1)
(2) 3C S C 6q 3q 2C S C 6q 3q
Left-hand increase (2)
Left hand decrease (3)
Remains the same (1)
Both capacitors must have the same potential difference.
(3) 2C S
2 C 6q 3q
(A) 1 (B) 2
(C) 3 (D) None
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21. Summary Capacitors in parallel and in series
Electric response of dielectric materials
atomistic view polarized atoms
dielectric constant
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