1. CHAPTER-25 Capacitance

2. Ch 25-2 Capacitance  Capacitor: Two electrically isolated conductors forms a capacitor.  Common example: parallel- plate capacitor consists of two parallel conducting plates of area A separated by a distance d.  The charge on each plate Q and potential difference across them V is related by: Q=CV where C is capacitance of the capacitor  Unit of capacitance : 1 Farad =1F=1C/1V

3. Ch 25-2 Capacitance  Charging a capacitor  Positive terminal of capacitor at higher (h) potential.  Negative terminal of capacitor at lower (l) potential.  In a complete circuit electrons moves through the wire under the electric field setup by the battery  E field of battery attracts electron from h terminal of capacitor making h positive  E field of battery send as many electrons to l terminal of capacitor making l negative  When h and l has same potential as the battery, no E-field in the wire and capacitor is fully charged.

4. Ch 25-3 Calculating the Capacitance Parallel Plate Capacitor  Parallel Plate capacitor:  Capacitance of the paralell plate capacitor C=q/V Calculating the charge q using Gauss’ law:  0  surf E.dA=q and  0 EA =q  Calculating the Potential Difference V V f -V i = -  i f E.ds If V= V f -V i angle between E and ds is 180 degrees then V=  - + E ds  Parallel Plate Capacitor V=  - + E ds=Ed and q=  0 EA Then C=q/V =  0 EA /Ed=  0 A/d C=  0 A/d

5. Ch 25-3 Calculating the Capacitance Cylindrical capacitor  A Cylindrical capacitor C=2  L  0 /ln(b/a)  A spherical capacitor: C=4  ab  0 /(b-a)  An isolated Sphere C=4  R  0

6. Ch 25-4 Capacitors in Parallel and Series  Capacitors in Parallel: equivalent capacitor has the same potential difference V as the actual capacitors and total charge q obtained by summing the charges stored on the capacitor. Then C eq =  C i  Proof: q=q 1 +q 2 +q 3 =C 1 V+C 2 V+C 3 V q=(C 1 +C 2 +C 3 )V=C eq V C eq =C 1 +C 2 +C 3 and q=q 1 +q 2 +q 3

7. Ch 25-4 Capacitors in Parallel and Series  Capacitors in Series : equivalent capacitor has the same charge q and total potential difference V obtained by summing the potential difference across the actual capacitors. 1/C eq =  (1/C i )  V=q/C eq =V 1 +V 2 +V 3 = q/C eq  =q/C 1 +q/C 2 +q/C 3 V=q(1/C 1 +1/C 2 +1/C 3 ) V=q/C eq C eq =1/  (1/C i )

8.  Energy Stored in a capacitor: Work done in charging the capacitor. E field between the plates opposes further charge transfer to charge plates  A capacitor with an initial charge q’ at each plate with potential difference V’ = q’/C across the plates.  Work done by external agent W in moving additional charge dq’ to the plates W appl =  0 q dW=  0 q V’dq’=  0 q (q’/C)dq’ =q 2 /2C  Potential Energy in the capacitor U= W appl U= q 2 /2C=CV 2 /2  Energy Density: Potential energy U per unit volume Parallel plate capacitor u=U/Ad=CV 2 /2Ad= (  0 A/d)V 2 /2Ad u= (  0 /2)V 2 /d 2 = (  0 /2)E 2 Ch 25-5 Energy Stored in an Electric Field of a capacitor

9.  Dielectric, an insulator that is inserted between the plates of a capacitor to increase the capacitance of the capacitor by a factor  then  C  =  C air where  is dielectric constant of the material and C air is capacitance of the capacitor with air between the plates.  Dielectric also used to limit the applied potential difference between the plates to a upper limit V max called breakdown potential Ch 25-6 Capacitors with a dielectric

10.  For a circuit with the battery:  When a dielectric is inserted the charge on the plates increases but V across the capacitor remains constant.  For a circuit without battery:  When a dielectric is inserted the charge on the plates remains constant but V across the capacitor plates decreases.

11. Suggested problems Chapter 25