Physics midterm question: comparing capacitor energies

Physics 205B Midterm 2, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 17.22

Two parallel plate capacitors have the same area, but different separation gaps and different amounts of charge. Determine which capacitor stores more electric potential energy, or if this is not possible to determine, discuss why. Explain your reasoning using the properties of capacitors, charge, electric potential, and energy.

Solution and grading rubric:

• p:
  Correct. Discusses how:
  1. as capacitance depends inversely on plate separation distance (with the same areas for both capacitors), the larger d for the second capacitor means that has a smaller capacitance; and
  2. the second capacitor has more charge stored on it, so with a smaller capacitance, it must have a larger potential difference;
  3. using electric potential energy EPE = (1/2)·Q·ΔV or Q²/(2·C), the second capacitor with a greater charge, greater potential difference, and smaller capacitance will store more electric potential energy.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Two of the three arguments in (p) are correct and complete.
  
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Only one of the three arguments in (p) are correct and complete.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 30882
Exam code: midterm02B1rD
p: 1 student
r: 11 students
t: 14 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1203):