PH213, W2012 – MIDTERM TWO TEST, Wednesday, Feb. 29, 2012

Directions: No books or notes or other outside help may be used during this exam. Graphing calculators are allowed. Wireless communication devices of any type (such as cellphones, palmtops, iPads, or portable computers)are not allowed. Make sure that the front page has your signature in the box at the right side, and has all the necessary information: last name, your student ID number, and the date. Fill the boxes at the top of Pages 1-4 (we will take care of the boxes on the righ side :o)) .

The work you present must be your own. There are 5 multiple choice questions – use the table on Page 1 for giving your answers. Then, there are three problems, # 6, 7 and 8. Please write the solution of each problem on a separate page: thesolution of problem 6 on Page 2, of problem 7 – on Page 3, and of problem 8 on Page 4. If you run out of space on a page, you may continue on the back side, but please make a clear mark on the bottom (e.g., “PLEASE TURN OVER”).

Question 1 (5 pts).

In order to measure the potential at the high voltage (HV) electrode of an electrostatic generator using a voltmeter whose upper range is much lower than the HV generated, N identical capacitors are series-connected. One end of the “chain” is connected to the HV electrode, and the other is grounded. The voltmeter measures the voltage of the last capacitor in the series, as shown in plot (a). Another identical capacitor is then connected in parallel to the last one in the the series, as shown in Plot (b).

After adding the parallel capacitor, the potential difference measured by the voltmeter is:

  1. One-half of that before adding the parallel capacitor;
  2. The same as before adding the parallel capacitor;
  3. Twice as high as before adding the parallel capacitor;
  4. (1 + 1/N) times the voltage measured before adding the parallel capacitor.

Question 2 (5 pts). Six rods of the same length and the same resistance R = 1Ω each are connected to form a tetrahedron. The equivalent resistance between any two vertices of the tetrahedron is:

  1. 1/6 Ω;
  2. 1/3 Ω;
  3. ½ Ω;
  4. 2/3 Ω.

Question 3 (5 pts). A capacitor of capacitance C = 10 000 μF is charged to a voltage V, and then disconnected from the voltage source. At t = 0 the capacitor terminals are connected to 2 kΩ resistor. The capacitor’s voltage decreases to the value of V/e (where e = 2.7183…) at:

  1. t = 2 s;
  2. t = 2.72 s;
  3. t = 20 s;
  4. t = 27.2 s.

Question 4 (5 pts). A one-meter wire of uniform thickness and of resistance R = 16 Ω is cut into two equal halves. Both halves are connected to a 48 V battery of negligible internal resistance, as shown schematically in Plot (a).

Another identical one-meter wire is cut into two pieces of 25 cm and 75 cm lengths. Both pieces are connected to another 48 V battery of negligible internal resistance, as displayed in Plot (b)..

The power dissipated in the circuit plotted in (b) is:

  1. Lower by 33.3% than the power dissipated in the circuit in Plot (a);
  2. The same as in the circuit in Plot (a);
  3. Higher by 33.3% than the power dissipated in the circuit in Plot (a);
  4. Higher by 66.7% than the power dissipated in the circuit in Plot (a).

Problem 6 (20 or 16 pts). You want to determine the EMF (i.e., the value ofE )and the internal resistance of a battery which has no marks on it. You have an ammeter, and two resistors with the resistance values of R1= 20 Ω and R2 = 40 Ω. When R1 is connected to the battery, the current is I1= 1.10 A, and when R2 is connected, the current is 0.574 A.

(a)Find the E value of the battery(7 or 5 pts);

(b)Find the internal resistance of the battery(7 or 5 pts);

(c)Find the “shortcut current” of the battery – i.e., the ammeter readings when it is connected directly to the battery terminals (assume that the ammeter’s resistance is negligibly small)(6 pts).

(answers to (a) and (b) obtained through step-by-step solving of the appropriate equations will be credited up to 7 pts. each; solutions obtained just by feeding in numbers to a calculator capable of solving equation systems will be credited up to 5 pts. each).

Problem 7 (25 pts). Two metal spheres (radii a and b) are very far apart but are connected by a thin wire. Their combined charge is Q.

(a)What is the charge on each?(13 pts);

(b)What is their absolute potential (i.e., relative to infinity)?(12 pts).

Problem 8 (30 pts). Consider a parallel-plate capacitor with plate area A and charge Q.

(a)What is the energy U stored in this capacitor, if the distance between the plates is d? (6 pts);

(b)Using the energy-work theorem, find the force acting on each plate(8 pts);

(c)Use and alternative method: find the force acting on one plate because of the E field arising from the charge on the other plate, and compare with the result you have obtained in (b) (8 pts);

(d)Compute the work done in separating the plates from essentially zero separation to a separation d(assume that Q remains unchanged). Compare theresult with that you have obtained in the (a)task(8 pts).