The SI unit of capacitance is the farad (F) = coulombs per volt,

3. Consider two conductors carrying charges of equal magnitude but of opposite sign, Such a combination of two conductors is called a capacitor. 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) = coulombs per volt,

4. Example 1 An electric potential of 5 V is applied across a capacitor of 20 x10-6 F, the electric charge Q acquires is

5. 26.2 CALCULATING CAPACITANCE Parallel-Plate Capacitors A parallel-plate capacitor consists of two parallel conducting plates, each of area A, separated by a distance d. When the capacitor is charged by connecting the plates to the terminals of a battery, the plates carry equal amounts of charge. One plate carries positive charge +Q, and the other carries negative charge -Q. The value of the electric field between the plates is

6. The capacitance of a parallel-plate capacitor is proportional to the area of its plates and inversely proportional to the plate separation

7. Example 2 A parallel-plate capacitor has an area A = 2 x 10-4m2 and a plate separation d = 1x10-3 m. Find its capacitance. C = 8.85 x 10-12 (C2/N.m2) . 2x 10-4(m2)/ 1x 10-3 (m) 1.77 x 10-12 F = 1.77 pF Example 3 The capacitance of two parallel plates with an area A and separation d is

8. Example 4 The capacitance of a parallel – plate capacitors having area 2 x10-4 m2 of each plate and separating distance of 5 m equals to

9. 2. The Cylindrical Capacitor A cylindrical capacitor consists of a solid cylindrical conductor of radius a and length surrounded by a coaxial cylindrical shell of radius b.

10. 3.The Spherical Capacitor A spherical capacitor consists of an inner sphere of radius a surrounded by a concentric spherical shell of radius b.

11. Other different capacitors shape

13. 26.3 COMBINATIONS OF CAPACITORS Parallel Combination Let us call the maximum charges on the two capacitors Q 1 and Q 2 . The total charge Q stored by the two capacitors is Q= Q1+Q2 Q2= C2 V Q1= C1 V The equivalent capacitor Q= Ceq V Ceq V= C1 V+ C2 V Ceq= C1 + C2

14. Parallel Combination V=V1=V2 and Q= Q1+ Q2

15. Series Combination Q=Q1=Q2 and V=V1+V2

16. Example : Find the equivalent capacitance between a and b for the combination of capacitors shown in Figure Fig 26-11, p.806

17. Example 6 Two capacitors C1=6 PF, and C2= 4 PF connected in parallel What is an equivalent capacitance C total= And when connected in series, what is an equivalent capacitance C1  c1 c2 a a b b    C2

18. Example: the equivalent capacitance between a and b is c1 c2 a b   if C1=C2 = 4 nF C1  C2 b a  If C1 = 4  F C2 = 5  F C3 = 8  F C3 

22. We see that a dielectric provides the following advantages: • Increase in capacitance • Increase in maximum operating voltage

24. Ex A parallel plate capacitor of geometrical dimensions of 2 cm by 2 cm separated by 2 mm thickness Of Mylar ( K= 3.2 ). Its capacitance is