A capacitor consists of two conductors that are close...
Transcript of A capacitor consists of two conductors that are close...
![Page 1: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/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/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/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/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/3.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 4: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/4.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 5: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/5.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 6: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/6.jpg)
Dielectric strength is the maximum field a dielectric can experience without breaking down.
![Page 7: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/7.jpg)
The molecules in a dielectric tend to become oriented in a way that reduces the external field.
![Page 8: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/8.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.
![Page 9: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/9.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 10: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/10.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 11: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/11.jpg)
Circuits Containing Capacitors in Series and in Parallel
Capacitors in parallel have the same voltage across each one:
![Page 12: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/12.jpg)
In this case, the total (equivalent) capacitance is the sum:
![Page 13: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/13.jpg)
Capacitors in series have the same charge:
![Page 14: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/14.jpg)
In this case, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance:
![Page 15: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/15.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 16: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/16.jpg)
The voltage across the capacitor increases with time:
This is a type of exponential.
![Page 17: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/17.jpg)
This curve has a characteristic time constant:
The charge follows a similar curve:
![Page 18: A capacitor consists of two conductors that are close …martinatsaints.pbworks.com/w/file/fetch/64408597/Capacitance.ppt.pdf · Capacitance A capacitor consists of two conductors](https://reader031.fdocuments.in/reader031/viewer/2022022607/5b87307d7f8b9a28238c383d/html5/thumbnails/18.jpg)
If an isolated charged capacitor is connected across a resistor, it discharges: