Physics midterm question: comparing same-energy, different potential capacitors

Physics 205B Midterm 2, spring semester 2019
Cuesta College, San Luis Obispo, CA

A capacitor is connected to a 1.5 V battery and a different capacitor is connected to a 6.0 V battery. Both capacitors store the same amount of electrical potential energy. Discuss why the capacitor connected to the 1.5 V battery has a larger capacitance than the capacitor connected to the 6.0 V battery. Explain your reasoning by using the properties of capacitors, charge, electric potential, and energy.

Solution and grading rubric:

• p:
  Correct. Discusses why the capacitor connected to the 1.5 V battery has a greater capacitance than the capacitor connected to the 6.0 V battery because:
  1. from EPE = (1/2)⋅Q⋅(ΔV), both capacitors store the same amount of electrical potential energy; such that the capacitor connected to the 1.5 V battery holds a larger charge than the capacitor connected to the 6.0 V battery; and
  2. from C = Q/ΔV, since the capacitor connected to the 1.5 V battery has a smaller potential difference and a larger charge than the capacitor connected to the 6.0 V battery; then the capacitor connected to the 1.5 V battery must have a larger capacitance.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically assumes that both capacitors have the same charge, and/or does not explicitly use the given fact that the capacitors store the same amount of electrical potential energy.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some attempt at applying 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 systematically applying properties of capacitors, charge, electric potential, and energy.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm02u7aH
p: 22 students
r: 1 student
t: 18 students
v: 0 students
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 2334):
Another sample "p" response (from student 1842), substituting in Q = C·ΔV into the electric potential energy equation: