summary Capacitance Parallel plates coaxial cables Earth Series

summary • Capacitance • Parallel plates, coaxial cables, Earth • Series and parallel combinations • Energy in a capacitor • Dielectrics • Dielectric strength

(25 - 12)

• Series combinations reduce the capacitance. Equal C reduce by the number involved. • In parallel the capacitance increases. v. A basket of 4 capacitors, each of C = 6 n. F. How can you arrange them to get a) 1. 5 n. F b) 2 n. F g) 2. 4 n. F c) 3 n. F h) 3. 6 n. F d) 4 n. F i) 4. 5 n. F j) 6 n. F e) 12 n. F k) 18 n. F f) 24 n. F

clicker All C’s are 8. 00 n. F. The battery is 12 V. What is the equivalent capacitance? a. b. c. d. e. 4 n. F 6 n. F 8 n. F 10 n. F 12 n. F

All C’s are 8. 00 n. F. The battery is 12 V. What is the equivalent capacitance? C 12 = 4 n. F C 123 = 12 n. F Q 123 = C 123 x V = 144 n. C Q 3 = C 3 x V = 96 n. C Q 12 = C 12 x V = 48 n. C U 123 = ½ C 123 V 2 = ½ x 12 x 10 -9 x 122 = 864 n. J U 1 = ½ C 1 V 12 = ½ x 8 x 10 -9 x 62 = 144 n. J = U 2 U 3 = ½ x 8 x 10 -9 x 122 = 576 n. F C 3 stores most energy, also the highest electric field and most charge, the most stressed part of the circuit.

Circuits • All capacitors being the same, rank the equivalent capacitances of the four circuits.

C 1 = C 3 = 8. 00 μF, C 2 = C 4 = 6. 00 μF, V = 12 V When the switch S is closed, how much charge flows through point P C 123 2. 4 µF, q = 28. 8 µC C 24 = 12 µF C 1234 = 3 µF q =36 µC Δq = 7. 2 µC

q -q V q' V -q' q V -q q V' -q (25 - 15)

q -q V q' V -q' q V -q q V' -q (25 - 16)

If the areas are A 1 and A-A 1. Effect of a dielectric : C κC C 123 2. 4 µF, q = 28. 8 µC C 24 = 12 µF C 1234 = 3 µF q =36 µC

The force on a filling dielectric as it is inserted between the parallel plates of a capacitor. x L With the battery connected, U 1 = ½CV 2 With the battery disconnected, U 2 = Q 2/2 C With the battery connected, since x is increasing downwards, a negative force is upwards, pushing the dielectric away. With the battery disconnected, the force is positive and pointed downwards, pulling in the dielectric. The force is proportional to (κ-1) and inversely to L.

A question What is the equivalent capacitance between the points A and B? A. B. C. D. E. 1 μF 2 μF 4 μF 10μF None of these A What would a 10 V battery do, i. e. how much charge will it provide, when it is connected across A and B? 40 μC B

Question • A parallel-plate capacitor has a plate area of 0. 3 m 2 and a plate separation of 0. 1 mm. If the charge on each plate has a magnitude of 5 x 10 -6 C then the force exerted by one plate on the other has a magnitude of about: A. 0 B. 5 N C. 0. 9 N D. 1 x 104 N E. 9 x 105 N The electric field = σ/2εo why?

Question • A parallel-plate capacitor has a plate area of 0. 3 m 2 and a plate separation of 0. 1 mm. If the charge on each plate has a magnitude of 5 x 106 C then the force exerted by one plate on the other has a magnitude of about: • A. 0 B. 5 N C. 9 N D. 1 x 104 N E. 9 x 105 N

A question • Each of the four capacitors shown is 500 μF. The voltmeter reads 1000 V. The magnitude of the charge, in coulombs, on each capacitor plate is: A. 0. 2 these B. 0. 5 C. 20 D. 50 E. none of

HITT A parallel-plate capacitor has a plate area of 0. 2 m 2 and a plate separation of 0. 1 mm. To obtain an electric field of 2. 0 x 106 V/m between the plates, the magnitude of the charge on each plate should be: A. 8. 9 x 10 -7 C B. 1. 8 x 10 -6 C C. 3. 5 x 10 -6 C D. 7. 1 x 10 -6 C E. 1. 4 x 10 -5 C