If the charge on each plate is 3 C , the distance between the plates is 3 m, and the area of each plate is 4 m²:

1. What is the capacitance of this capacitor?

2. What is the potential difference DV_AB ?

3. What is DV_AB = V_B-V_Ain the figure below?

4. What is the work required to move a 2 C charge from A to B in the figure above?

5. An isolated large plate capacitor (not connected to anything ) originally has potential difference of 1000 volts with an air gap of 4 mm. Then a metal slab 2 mm thick, is centered between the plates.

Calculate the following poential differences.
a. V1 - V2
b. V2 - V3
c. V3 - V4
d. V1 - V4

6. Assuming all the bulbs are identical, when the switch is thrown, what happens to the brightness of :
a. Which is brighter B1 or B4 ?
b. Which is brighter B2 or B4 ?

7. A certain capacitor made up of two circular disks of cross-sectional area A , and distance s between them is connected to a 10 V battery and receives a total charge Q on the plates. What happens to the capacitance on the plates when :

a) The cross sectional area A is doubled ?
b) The distance between the plates s is doubled?
c) The voltage on the plates is doubled?
d) A piece of plastic with dielectric constant 5 is inserted between the plates?
e) 5 Pts Bonus: A piece of metal half the width of the gap is inserted between the plates?

8. If an electron is moved from a point where the electric potential is 10 V to a point where the electric potential is 60 V does its potential energy increase or decrease?

9. If the electric potential from one end of a 40 cm length of wire to the other is 5 volts, what is the electric field inside the wire?

10. Two nuclei, each of mass m and charge q, are travelling straight toward each other. They each have an initial speed of v when they are far apart. As they approach they slow down and come to a momentary halt a distance d from each other, before rebounding straight away from each other. Ignoring the effects of gravity,

a. Write an energy equation that could be solved for the distance d of closest approach.
b. Solve the equation for d in terms of q, v and m.

11. a. If the current through a battery is doubled, by what factor is the battery power output increased?
b. If the current through a resistor is doubled, by what factor is the power dissipation increased?

12. A battery with negligible internal resistance is connected to a resistor. The power produced in the battery and the power dissipated in the resistor both are P1.

Another resistor of the same kind is added, so the circuit consists of a battery and two resistors in series.

(a) In terms of P1, now how much power is dissipated in the first resistor?
(b) In terms of P1, now how much power is produced in the battery?
(c) The circuit is rearranged so that the two resistors are in parallel rather than in series. In terms of P 1, now how much power is produced in the battery?

13. Find the total resistance between the points a and b of the configuration below.

14. Find the total capacitance between the points a and b in the figure below.

15. a. Find the system of equations that will obtain current in each of the resistors in the figure below.

b. Find the current in each of the resistors in the figure.

16. If the current in the wire while charging the plates obeys the formula I = 6 - 4t sin t2 , where t is time in seconds, how much charge builds up on the plates of the capacitor below in the first 3 seconds after the switch is thrown?