2000 February 25 Exam I Physics 106

Circle the letter of the single best answer. Eachquestion is worth 1 point

Physical Constants:

proton charge = e = 1.60 × 10−19 Cproton mass = mp = 1.67 × 10−27 kgelectron mass = me = 9.11 × 10−31 kgpermittivity of free space = ǫ0 = 8.85 × 10−12 F/mCoulomb constant = ke = 9 × 109 N · m2/C2

Faraday constant = 9.65 × 104 Cspeed of light = c = 3 × 108 m/sRydberg energy = Ry = 2.18 × 10−18 J = 13.6 eV

1. A negatively charged rod approaches a previ-ously neutral conducting sphere. Which pic-ture best displays the arrangement of the sur-face charges on the sphere?

−−−− A

−+

++ B

−+

++ C−

−−

− D−−−

++

+

2. The sphere described the previous problem isgrounded. Which picture now best displaysthe arrangement of the surface charges on thesphere?

−−−− A

−+

++ B

−+

++ C−

−−

− D

3. An electron is moving at high speed through afield-free region. In enters (and soon exits) a re-gion in which the electric field points up. Whichpath best represents the path of the electron?

uniform E field

uniform E field

A

B

C

D

4. There is no net charge on a conducting sphere.The force between a positively charged rod andthe sphere is:

(a) zero

(b) attractive

(c) repulsive

(d) at first repulsive, but then attractive

5. The electric field just outside of a positivelycharge conductor may be best characterized bywhich combination of the following conditions:

I. tangent to the surface

II. zero magnitude

III. largest on the parts of the conductor atthe highest voltage

IV. largest on the parts of the conductor withthe smallest radius of curvature

V. largest on the parts of the conductor withthe largest surface charge density

(a) I, III, IV

(b) IV, V

(c) II

(d) II, IV, V

6. In a thundercloud there may be an electriccharge of +100 C at the top of the cloud and−100 C near the bottom of the cloud. Thetop and bottom of the cloud are separated by3 km. The electric force between these two setsof charges is most nearly:

(a) 10,000,000 N

(b) 1,000,000 N

(c) 100,000 N

(d) 10,000 N

7. A 10 V battery is connected between two largeparallel plates separated by 1 mm. The magni-tude of the electric field between the plates ismost nearly:

(a) 9 × 104 V/m

(b) 10,000 N/C

(c) 9 × 102 V/m

(d) 9 × 106 V/m

8. Three capacitors of capacitance 1 µF, 2 µF, and3 µF are connected in parallel. The combinedcapacitance is most nearly:

(a) 6 µF

(b) 0.17 µF

(c) 0.55 µF

(d) 0.67 µF

9. A 6 µF and a 3 µF capacitor are connected inseries and charged with a 9 V battery.

(a) The voltage drop across the 6 µF capacitoris half the voltage drop across the 3 µFcapacitor.

(b) The charge stored on the 6 µF capacitoris equal to the charge stored on the 3 µFcapacitor.

(c) Together the two capacitors act like one2 µF capacitor.

(d) All of the above are true.

10. 9 V is placed across the terminals of a 3 µFcapacitor. How much charge is (most nearly)stored on the capacitor?

(a) 0.3 µC

(b) 3 µC

(c) 30 µC

(d) 3 × 106 C

11. For the capacitor of the previous problem, ap-proximately how much energy is stored in thecapacitor?

(a) 3 µJ

(b) 27 µJ

(c) 41 µJ

(d) 122 µJ

12. A parallel plate capacitor has been “charged”with a charge Q. A dielectric slab (dielectricconstant κ > 1) can exactly fit between theplates. If the dielectric is inserted

+Q

−Q :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

V

Dielectric κ

(a) the charge on the plates and the voltagewill increase.

(b) the capacitance will increase and the volt-age will decrease.

(c) the electric field between the plates willincrease.

(d) the capacitance and the electric field be-tween the plates will decrease.

13. A 60 W light bulb is designed to operate at120 V. The resistance of this bulb when oper-ating is most nearly:

(a) 2 Ω

(b) 20 Ω

(c) 200 Ω

(d) 2 kΩ

14. Replacing a wire resistor with another of thesame material and length but with three timesthe diameter will have the effect of changing theresistance by what factor?

(a) 1

9

(b) 1

3

(c) 3

(d) 9

15. A 500 W heater carries a current of 4 A. Howmuch does it cost to operate the heater for 30minutes if electrical energy costs 6/c per kW·hr

(a) 1.5 /c

(b) 6 /c

(c) 12 /c

(d) 24 /c

16. Which process will double the heat given off bya resistor?

(a) Increasing the voltage by a factor of√

2.

(b) Doubling the current while making the re-sistance half as big.

(c) Doubling the voltage while making the re-sistance twice as big.

(d) All of the above.

17. The following three appliances are connectedto a 120 V house circuit: (i) 1200 W toaster,(ii) 600 W microwave, and (iii) 120 W lamp.What is the smallest fuse you could use and stilloperate all of these devices at the same time?

(a) 10 A

(b) 15 A

(c) 20 A

(d) 25 A

18. In terms of units the equation P = IV reads:

(a) J/s = C/s × J/C

(b) W = Ω × V

(c) W = C/s × N/C

(d) A = Ω × V

19. As you saw in lab, if you increase the volt-age across a light bulb, the light bulb goesfrom non-luminous to luminous. If you wereto increase the voltage still further you wouldmelt the metal filament and the bulb would be“burned out”. As you begin to increase thevoltage across the light bulb:

(a) the drift velocity of the electrons increases

(b) the resistance of the filament increases

(c) the electrical power consumed by the fila-ment increases

(d) all of the above

20. What is the current through the 6 Ω resistor?

4 Ω 6 Ω24 V

(a) 3 A

(b) 10 A

(c) 2.4 A

(d) 4 A

21. What is the current through the 6 Ω resistor?

4 Ω

6 Ω

24 V

(a) 3 A

(b) 10 A

(c) 2.4 A

(d) 4 A

22. If you measure the voltage across a particularbattery’s terminals with a voltmeter you read6 V. However if you read the voltage acrossits terminals when it is powering a light bulbknown to be drawing 0.5 A, you find 5.5 V.The internal resistance of the battery is:

(a) 6 Ω

(b) 3 Ω

(c) 1 Ω

(d) 0.5 Ω

23. The same components are used to make a seriescircuit of 10 Ω and 20 Ω resistors and a parallelcircuit. In each circuit, which resistor drawsthe most electrical power?

10 Ω 20 Ω

10 Ω

20 Ω

(a) The 10 Ω draws the most power in theparallel circuit; the 20 Ω draws the mostpower in the series circuit.

(b) The 20 Ω draws the most power in theparallel circuit; the 10 Ω draws the mostpower in the series circuit.

(c) The 10 Ω draws the most power in bothcircuits.

(d) The 20 Ω draws the most power in bothcircuits.

24. An alien electronic device is found sitting on theground near Area 51. In an unknown languageit is labeled “Danger Acme K-Bomb”. Its twoterminals are wired into a circuit as shown be-low. The ammeter reads 0.1 A, the voltmeter isabout to be attached. What will the voltmeterread?

100 ΩA

Danger

Acme

K-bomb

120 V

V

(a) 120 V

(b) 110 V

(c) 100 V

(d) You can’t say without further information

25. Which of the four identical bulbs will shine thebrightest in the below circuit?

A B

CD

(a) A

(b) B

(c) C

(d) D

26. In below plots the elliptical loops are equipotentials. Adjacent loops have the same voltage difference(e.g., consecutive loops might be at voltages: 0, 10, 20, 30, . . . volts.). At each point corresponding tothe tail of the vector the electric field has been calculated and is displayed as an arrow. Which plotproperly displays the relationship between electric potential (voltage) and electric field?

(a) -3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

(b) -3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

(c) -3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

(d) -3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

The following questions are worth 5 pts each

27. As shown below three charges are arranged in an equilateral triangle with side 50 cm. Find themagnitude of the electric field vector at the spot marked with an X (i.e., the midpoint of the horizontalsegment).

q3 = 3 nC

q2 = 5 nCq1 = 8 nC

s = 50 cm

28. Find the voltage at the spot marked with an X in the above figure.

29. An electron moving only the influence of electric forces (i.e., no gravity, no “friction”) initially findsitself moving with a speed of 6 × 106 m/s in a region where the voltage is 100 V. When it enters aregion where the voltage is 200 V, how fast is the electron moving?

30. When plugged into a 120 V household circuit an immersion heater draws 2 A. The immersion heateris used to warm 250 g of water (c = 4186 J/kgC). How long does it take for the heater to bring 20Cwater to a boil?

31. (This problem counts as two problems.) Find the current in each leg of the following circuit. (Pleaseclearly label which current goes with which leg.)

12 V

2 Ω

18 V

6 Ω

6 V