practice_exam_1_key

PH102-001 Practice Exam 1 Solutions Spring, 2010

Use the scan sheet to bubble in your answers. Write the test version (a or b) on the scan sheet. Also, circle the answers on this sheet and show your work in the space provided.

1. Two identical charges are a certain distance apart. The force on each charge is F. If you double each of the charges and also double the separation, what is the new force?

(a) 2F (b) 4F (c) F/2 (d) F/4 (e) F

F r q k F r

q k F ===2222

)2()2(',

2. If the original potential energy of the charges in problem 1 is PE, what is the potential energy after doubling the charges and doubling the separation?

(a) 2PE (b) 4PE (c) PE/2 (d) PE/4 (e) PE

PE r q k PE r

q k PE 22)2(',2

2===

3. Find the magnitude of the electric field at point P due to the two point

charges.

(a) 1 x 105 N/C (b) 2 x 105 N/C (c) 4 x 105 N/C (d) 3 x 104 N/C (e) 9 x 104 N/C

C N e e e r q k E E E E o x x /52)5.0()

3.0()62()99(2)5.0(260cos 2221121=?===+=

4. A proton is released from rest in a region where the electric field is 2000 V/m. What is its speed after 5 μs?

(a) 9.6 x 105 m/s (b) 3.3 x 106 m/s (c) 1.9 x 1011 m/s (d) 5.4 x 103 m/s (e) 6.1 x 107 m/s

s

m e e s m e at v s m e e e m qE m F a /56.9)65)(/1192.1(/1192.12767.1/)2000)(196.1(//22

=?===??===

q 1 = 2 μC q 2 = -2 μC

5. The cube to the right has edge length 0.5 m. A horizontal electric

field is perpendicular to the left and right faces of the cube and is

parallel to the other faces. At the left face E = 3 x 104 V/m and at the

right face E = 2 x 104 V/m. What is the charge contained inside the

cube? i

(a) 1.25 x 104 C (b) -5 x 10-4 C (c) 8.85 x 10-12 C (d) -2.2 x 10-8 C (e) 4.3 x 10-6 C

C e e e e A E A E q E in 821.2)5.0)(4243)(1285.8()(22100??=+??=+?ε=Φε=

6. A sphere of radius R = 0.3 m has a uniform charge Q = 5 μC. A particle with charge q = 0.2 μC and

mass m = 4 x 10-5 kg is released from rest on the surface of the sphere. What is the kinetic energy of the particle after it has moved 0.1 m away from the surface? Assume that the sphere doesn’t move.

(a) 9 x 10-4 J (b) 7.5 x 10-3 J (c) 3.75 x 104 J (d) 0.023 J (e) 5.1 J

J

e e e e r r kqQ r qQ k r qQ k PE PE PE KE

f i f i f i 35.7)4.013.01)(65)(62.0)(99()11(?=???=?=?=?=Δ?=Δ

7. Which of the following statements is false regarding an isolated conductor in equilibrium?

(a) Any excess charge resides on the surface.

(b) The electric potential is constant everywhere inside the conductor.

(c) The electric field is zero everywhere inside the conductor.

(d) More charge per unit area collects on the sharper parts of the surface than on the flatter parts.

(e) The electric field just outside the surface is greater near the flatter parts than near the sharper parts.

8. In the circuit to the right, V = 12 volts, C 1 = 2 μF and C 2 = 4 μF.

What is the voltage across C 1? (a) 12 V (b) 4 V (c) 8 V (d) 6 V (e) 2 V

V

F C C Q V C C V F V C Q F C C C C C s s s 82/16/16)12)(33.1(33.14

2)4)(2(11112121=μμ===μ=μ==μ=+=+=

V C 1 C 2

9. A wire has resistivity 1.1 x 10-6 Ω-m. It is 5 m long and has radius 1 mm. If the wire carries a current of 7.5 A, what is the voltage difference between the ends of the wire?

(a) 1.75 V (b) 0.23 V (c) 5.5 V (d) 13.1 V (e) 0.09 V

V

IR V e e r l A l R 1.13)75.1)(5.7(75.1)

31()5()61.1(22===Ω=?π?=πρ=ρ=

10. A 24-volt battery is connected across a 600-Ω resistor. How many electrons flow through the resistor in a 1-hour period?

(a) 144 (b) 4 x 106 (c) 9 x 1020 (d) 6 x 1023 (e) 5.4 x 1012

20

9196.1/144/144)3600()600()24(e e e q N C t R V t I q =?=Δ===Δ=Δ=Δ

11. What is the equivalent resistance between points a and b in the

circuit to the right?

(a) 75 Ω (b) 45 Ω (c) 30 Ω (d) 20 Ω (e) 15 Ω Ω

=++=+++=+++++++=30915693030)30)(30(69)1020()1020()1020)(1020(6R

12. What is the current in resistor R 3 to the right? (a) 2.8 A (b) 6 A (c) 4 A (d) 2 A (e) 1 A A

R V I V IR V A

R V I R R R R R R eq 260/120/120)20)(6(660/360/6020406030)60)(30(40323323233

2321==========+=++=++=

13. A 100-μF capacitor is charged to 20 V and then discharged through a 500-k Ω resistor. How long does it take for the capacitor voltage to reach 4 volts?

(a) 80 s (b) 5 s (c) 0.04 s (d) 100 s (e) 0.9 s

s

e e RC t RC t e e e V V RC t RC t RC t 80)2.0ln()41)(55()2.0ln(/)ln()2.0ln(,204,///0=??=?=?====??? V =360 V R 1 = 40 Ω R 2 = 30 Ω R 3 = 60 Ω 9 Ω 6 Ω 20 Ω 10 Ω 10 Ω 20 Ω a b

14. A 60-W bulb is designed to operate from a 120-V source. What would be the power dissipated by each bulb if two 60-W bulbs were connected in series across a 120-V source?

(a) 15 W (b) 30 W (c) 60 W (d) 90 W (e) 120 W

)15)240()25.0('',25.0480/1202/',(15240/)60(/'',24060/)120(/,/2222222W R I P A R V I Or W

R V P series In P V R R V P =========Ω

====

15. What is the current in the 2 Ω resistor to the right?

(a) 5 A (b) 8 A (c) 3 A (d) 7 A (e) 1.5 A

A

I I I I cw goes I assuming left,lower from cw Going V 5.14/60

4)1(2)2(12)1(,0

===????+?∑=Δ

16. What is the direction of the current?

(a) right (b) left (c) up (d) down (e) zero

Useful numbers:

Coulomb force constant = k = 9 x 109 N ?m 2/C 2

Proton charge = 1.6 x 10-19 C = - electron charge

Proton mass = 1.67 x 10-27 kg

Electron mass = 9.11 x 10-31 kg

Permittivity of free space = ε0 = 8.85 x 10-12 C 2/N ?m 2

μ (micro) = 10-6

k (kilo) = 103 12 V 2 V 2 Ω 1 Ω 4 V

1 Ω