PHY 132 First Midterm, 2/2002, L. Mihaly 

Remove everything from work area, except this exam, your one page of handwritten notes and your calculator. Wait for instruction to start. Use the paper provided for all work (back side is OK), ask for empty sheets if you need more. When finished, copy all results to this (front) page. Hand in all your work.

Leaving the exam room: Ask for permission. Do not talk to anyone outside, do not take notes or the exam sheet with you. Leave the room during the last 15 minutes ONLY if you are finished and do not want to return.

Scores: Problems 1,2,3: 10 points for correct answer, partial credit possible. Problems 4-7: 5 points each, no partial credit, no guessing. The graders may check your solution to see if the work handed in justifies your choices in the multiple choice questions.

Complaints: The solutions will be posted on the course WEB page. The graded exam will be handed back to you by your recitation instructor. If you feel that a mistake was made, return the exam and a brief written statement of your grievance to your recitation instructor. Except for trivial mistakes (like incorrect addition of the scores by the grader), the returned exam will be accepted only on the same day that you received the graded exam in recitation. Preferably, you should ask for the re-grading at the end of the recitation session. Do not change your solution. If you make notes on the exam sheet, use a writing instrument that is very different from the pen/pencil used during the exam. The contested exams may be compared to a xerox copy made by the grader. If partial credit is contested, the whole exam will be re-graded. Your grade may go up, down or remain unchanged.

Copy your results here

 

Copy over the numbers and units, direction of vectors, etc.

 

1 a.) b.) c.)

 

 

 

2 a.) b.)

3

 

 

 

Circle the correct answer

 

4 A B C D E F

 

5 A B C D E F

 

6 A B C D E F

 

7 A B C D E F

 

 

1. A light bulb has a resistance of 55W and it is connected to an ac line of Vrms=120V (150V). a.) What is the average power? What are the b.) maximum and c.) minimum values of the instantaneous power?

Average: P=Vrms2/R=262W (409W)

Minimum: When the voltage is zero, the power is zero. That is the minimum value.

Maximum: From Pmax=V02/R, where V0=1.41Vrms is the maximum (peak) voltage, we get Pmax=2P=524W (818W). For simple ac voltage the maximum power is always twice the average.

2. In the circuit shown in the Figure the values of the capacitances are C1=15mF (24mF), C2=C3=25mF, and the battery provides V=14.0V. a.) What is the equivalent capacitance? b.) What is the total energy stored in the capacitors?

From 1/Cs=1/C2+1/C3 we get the equivalent of C2 and C3 (in series): Cs=12.5mF. This is parallel to C1, yielding Ceq=27.5mF (36.5mF) . The total energy is U=1/2 Ceq V2=2.7mJ (3.6mJ).

3. A flat disc of radius R=0.60m (0.9m) is charged with uniform surface charge density. The total charge on the disc is Q=3.0mC. Assuming that the potential is zero at large distances from the disc, what is the potential at the center? (Note: A table of integrals is enclosed. Most likely you will not need to use it.)

The surface charge density is s=Q/pR2. The charge stored in a ring of width dr, at a distance r from the center is dQ=s(2pr)dr= 2Qr dr /R2. The contribution to the potential in the center is dV=(1/4pe0) dQ /r=(1/2pe0)Q dr /R2. This quantity is independent of r, and therefore the integration is very simple. The total potential is

V=(1/2pe0)Q/R2 * Integral (from zero to R) dr =

(1/2pe0) Q/R=45kV (30kV).

4. Two charges of +q and two charges of -q are placed on the corners of a square of side a, so that the like charges are on diagonally opposite corners. How much work is done if a charge Q is brought from infinity to the center of the square? (q = 3.2mC, a = 1.3m, Q = 6.2mC.)

A 0.000 J

B 0.097J

B 0.137 J

C 0.390 J

D 0.549J

E none of the above

The work is exactly zero. The center of the square is of equal distance from the two positive and the two negative charges, and the total electric potential is zero.

5. A very long straight wire has charge per unit length 3.00 x 10-10 C/m. What is the electric field at a distance of 10.8m from the wire?

A 0.023N/C

B 0.046N/C

C 0.5N/C

D 1.0N/C

E none of the above

E = l/2pe0r= 0.5N/C

6. A wire is pulled until it is elongated to 1.5 times of its original length. What happens to its resistance? (Assume that the cross section remains uniform.)

A increases by a factor of 1.5

B decreases by a factor of 1.5

C increases by a factor of 2.25

D decreases by a factor of 2.25

E increases by a factor of 4.00

F decreases by a factor of 4.00

The length is increased, and the cross section is decreased by the same factor. The resistance increases by a factor of 1.52=2.25

7. The typical lightning bolt releases about 109J energy in about 0.2s time. The potential difference is about 5 x 107V. Estimate the current in the lightning.

A 105A

B 104 A

C 103 A

D 102 A

E 10 A

F 1 A

The current is I=Q/t, and the charge is Q=U/V. We get I=U/Vt=100A.

Fundamental constants: