==~~~~~--

c v·

Potential and Field . C H i\ P T E R 30 30-7

30.5 Capacitance and Capacitors,. ..•. ~ .•••.•••.• >;"' •• "' •• ,\,."" ••.••

30.6 The Energy Stored in a Capacitor

16. A parallel-plate capacitor with plate separation d is connected to abattery that has potential difference Ll Vbat. Without breaking any ofthe connections, insulating handles are used to increase the plateseparation to 2d.a. Does the potential difference Ll Vc change as the separation

increases? If so, by what factor? If not, why not?

__ ,--_1 d

b. Does the capacitance change? If so, by what factor? If not, why not?

IIiIII

Ic. Does the capacitor charge Q change? If so, by what factor? If not, why not? I'

17. For the capacitor shown, the potential difference Ll Vab between points aand b is

aa. 6 Vd.6· tan 30° V

Explain your choice.

b. 6 . sin 30° V

e. 6 . cos 30° V

c. 6/sin 30° Vf. 6/cos 30° V

6Vb

,I;

18. Rank in order, from largest to smallest, the potential differences (~Vdl to (~Vd4 of thesefour capacitors.

jO-8 CHAPTER 30 . Potential and Field

I Qillc~

11

~2C~_ -Q

2

I 2Q

c~

31

I 2Q

2C~

Order:

Explanation:

19. Each capacitor in the circuits below has capacitance C. What is the equivalent capacitance of the group

of capacitors?

b.a.

c.~

d. ±=c Ceq =L l

Cel] =I T T TT

e.~

f. ~

~=r::: =r:::

~

Ceq =

~ ICeq =

I.

"tl

".j

Potential and Field . C H A PH R 30 30-9

, 20. Rank in order, from largest to smallest, the equivalent capacitances (Ceq) I to (Ceq)4 of these four groups. of capacitors.

c c

c c c1HH~c c

H

... ,'.;

c

c2 c 3 c 4

·1

Order: ':

Explanation:

I

I

IIII

,21. Rank in order, from largest to smallest, the energies (U c) I to (U d4 stored in each of these capacitors.

i

':j.'

+1+2CTlM , 1 +4ctlavr-'Order~- ..I

I Explanation:

,,,

.j

I

.1

30.7 Dielectrics22. An air-insulated capacitor is charged until the electric field strength inside is 10,000 Vim, then

disconnected from the battery. When a dielectric is inserted between the capacitor plates, the electricfield strength is reduced to 2000 V1m.a. Does the amount of charge on the capacitor plates increase, decrease, or stay the same when the

dielectric is inserted? If it increases or decreases, by what factor?1''---- ...

b. Does the potential difference between the capacitor plates increase, decrease, or stay the same whenthe dielectric is inserted? If it increases or decreases, by what factor?

['''----II

23. The plates of an air-insulated capacitor are charged to ± 100 ne, then left connected to the battery.When a dielectric is inserted between the plates, the charge on the plates increases to ±500 ne.

a. Does the potential difference across the capacitor increase, decrease, or stay the same when thedielectric is inserted? If it increases, by what factor?

,- ---

b. Does the electric field strength inside the capacitor increase, decrease, or stay the same when thedielectric is inserted? If it increases, by what factor?

24. The gap between two capacitor plates is partially filled with a dielectric. Rankin order, from largest to smallest, the electric field strengths EI' £2, and E3 atpoints 1, 2, and 3.[--()~der:

I Explanation:

I