Physics final exam question: voltmeter reading of leaking capacitor

Physics 205B Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA

A capacitor is made from two parallel metal plates, and is charged with equal amounts of opposite charge. Both capacitor plates slowly lose their charge, due to being exposed to humid air. Discuss why the voltmeter reading attached to the capacitor decreases as this happens. Explain your reasoning by using the properties of capacitors, charge, electric potential, and energy.

Solution and grading rubric:

• p:
  Correct. Explains why the voltmeter reading will decrease as the capacitor plates lose their charge, by discussing:
  1. that the capacitance must remain constant, as the plate area and the spacing between the plates remain constant; and
  2. because capacitance remains constant, then charge and voltage difference are proportional to each other, and thus a decrease in charge results in a decrease in voltage difference.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Does not explicitly discuss (1).
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying the properties of capacitors, charge, electric potential, and energy.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying the properties of capacitors, charge, electric potential, and energy.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 7 students
r: 8 students
t: 1 student
v: 5 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 4447):