![Page 1: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/1.jpg)
Capacitance A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.
![Page 2: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/2.jpg)
a) Parallel-plate capacitor connected to battery. (b) is a circuit diagram.
![Page 3: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/3.jpg)
Some Uses of Capacitors
• Energy storage • Pulsed power and weapons • High-pass and low-pass filters • Sensing
![Page 4: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/4.jpg)
When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage:
The quantity C is called the capacitance.
Unit of capacitance: the farad (F)
1 F = 1 C/V
Q= Charge (C), and V= voltage (V)
![Page 5: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/5.jpg)
The capacitance does not depend on the voltage; it is a function of the geometry and materials of the capacitor.
For a parallel-plate capacitor:
C= Capacitance, A= area, d= distance between the plates, and = permittivity of free space
= 8.85x10-12 C2/N·m2 ∈0
![Page 6: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/6.jpg)
Example: a) Calculate the capacitance of a capacitor whose plates are 20
cm x 3.0 cm and are separated by a 1.0 mm air gap. b) What is the charge on each plate if the capacitor is
connected to a 12 V battery? c) What is the electric field between the plates? (recall
electrostatics)
![Page 7: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/7.jpg)
Solution: a) = 5.31x10-11 F = 53.1 pF
b) = 6.4x10-10 C
c) E = Vd
= 1.2x104 V/m
![Page 8: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/8.jpg)
Dielectrics
A dielectric is an insulator, and is characterized by a dielectric constant K.
Capacitance of a parallel-plate capacitor filled with dielectric:
![Page 9: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/9.jpg)
Dielectric strength is the maximum field a dielectric can experience without breaking down.
![Page 10: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/10.jpg)
The molecules in a dielectric tend to become oriented in a way that reduces the external field.
![Page 11: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/11.jpg)
This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential. The capacitance increases with the addition of the dielectric.
![Page 12: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/12.jpg)
Storage of Electric Energy in a Capacitor
A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor.
![Page 13: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/13.jpg)
The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field:
The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful!
![Page 14: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/14.jpg)
Circuits Containing Capacitors in Series and in Parallel
Capacitors in parallel have the same voltage across each one:
![Page 15: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/15.jpg)
In this case, the total (equivalent) capacitance is the sum:
![Page 16: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/16.jpg)
Capacitors in series have the same charge:
![Page 17: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/17.jpg)
In this case, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance:
![Page 18: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/18.jpg)
Example: Find the total (equivalent) capacitance, in terms of C, for the circuit below. Each capacitor has capacitance C.
Answer: 9/10 C
![Page 19: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/19.jpg)
Activity: Construct the circuit below using the sim “Circuit Construction Kit (AC+DC)” on the website phet.colorado.edu. a) Predict what will happen to current and voltage measured by the meters once the switch is closed. Close the switch and see how your predictons faired. b) Examine how the resistance, capacitance, and voltage of the battery effect the time for charging the capacitor. State conclusions.
Battery
resistor
switch
capacitor
![Page 20: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/20.jpg)
Activity: An uncharged capacitor is in a circuit as shown. What happens to the currents measured by ammeters A1 and A2 when the switch is closed? Predict what will happen.. Explain your observations.
A1
A2
uncharged!capacitor
swtich
R R
R
![Page 21: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/21.jpg)
Solution: Kirchoff’s laws must apply at every stage even if there is a varying current or voltage.
![Page 22: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/22.jpg)
Charging and Discharging of a Capacitor When the switch is closed, the capacitor will begin to charge.
How do you think the value of resistor and the capacitor might affect how rapidly a capacitor charges?
![Page 23: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/23.jpg)
The voltage across the capacitor increases with time:
This is a type of exponential.
![Page 24: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/24.jpg)
This curve has a characteristic time constant:
The charge follows a similar curve:
![Page 25: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/102364606/Capacitance PHAP... · Capacitance A capacitor consists of two conductors](https://reader031.vdocument.in/reader031/viewer/2022022018/5b87307d7f8b9a28238c3843/html5/thumbnails/25.jpg)
If an isolated charged capacitor is connected across a resistor, it discharges:
V =V0e−tRCAlso
èè