Physics midterm question: same charge, same gap, different area capacitors

Physics 205B Midterm 2, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 17.109

Two parallel plate capacitors have different areas, but the same separation gaps and the same charge. Discuss 
why the smaller area capacitor stores more electric potential energy. Explain your reasoning using the properties of capacitors.

Solution and grading rubric:

• p:
  Correct. (1) As capacitance is proportional to plate area (with the same separation distance for both capacitors), the smaller area for the first capacitor means that has a smaller capacitance. (2) The two capacitors have the same charge stored on them, so the first capacitor with a smaller capacitance must have a larger potential difference. (3) Using electric potential energy U_E = (1/2)∙Q∙(ΔV), the first capacitor with the greater potential difference stores 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:
Sections 30882
Exam code: midterm02w1Ig
p: 18 students
r: 8 students
t: 6 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 4444):