1. Capacitance�and�Dielectrics
Definition of Capacitance
Calculating Capacitance
Combinations of Capacitors
Energy Stored in a Charged Capacitor
Capacitors with Dielectrics

2. Definition of Capacitance
Two  conductors  carrying  charges  of equal magnitude  but  of  opposite sign is a capacitor
The conductors are called plates
The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between  them:
The SI unit of capacitance is the farad (F)

3. Calculating Capacitance
Parallel-Plate Capacitors
It consists of two parallel plates with area A separated by distance d
One plate carries a charge Q, and the other carries a charge Q
If A is large, then larger Q can be distributed over A (expectation : capacitance proportional to A)
If d is increased, the charge decreases (capacitance  to be  inversely proportional to ).

4. Parallel-Plate Capacitors
Suppose the charge density is
Using Gauss’s law, the electric field is
Potential difference between the plates equals Ed
The capacitance

6. Cylindrical Capacitors
The potential difference between A and B

7. Spherical Capacitors
The potential difference
The capacitance

8. Symbol

9. COMBINATIONS OF CAPACITORS
Parallel Combination
 the individual potential differences across capacitors connected in parallel are all  the  same and are equal to the potential difference applied across the combination.
The total charge Q stored by the two capacitors is
And
Thus

10. Series Combination
The charges on capacitors connected in series are the same
The voltage across the battery  terminals is split between the two capacitors:
And
We get
Finally

11. Example: Combining the capacitors

12. Energy Stored in a Charged Capacitor
Suppose we charge the capacitor and q is charge at some instant during charging process. The potential difference is
 To transfer an increment  of  charge  dq, the work
Total work Or

13. Energy Density Energy in capacitor We may get
Thus energy per unit volume (energy density)

14. CAPACITORS WITH DIELECTRICS
A dielectric is a non conducting material, such as rubber, glass, or waxed paper
When a dielectric is inserted between the plates of a capacitor, the capacitance increases
If  the dielectric completely fills  the  space between  the plates,  the capacitance  increases  by  a  dimensionless  factor  k�,  which  is  called  the  dielectric  constant
The voltages with and without the dielectric are related by the factor k as follows
Because the charge Q0 on the capacitor does not  change, we conclude that the capacitance must change to the value

15. CAPACITORS WITH DIELECTRICS(2)
A dielectric provides the following advantages:
Increase in capacitance
Increase in maximum operating voltage
Possible mechanical  support between  the plates, which  allows  the plates  to be close together without touching, thereby decreasing d and increasing C

16. Dielectric Constants