## 20160508

### Physics midterm question: inserting new dielectric into capacitor

Physics 205B Midterm 2, spring semester 2016
Cuesta College, San Luis Obispo, CA

The insulating material between the plates of a capacitor that is connected to an ideal emf source is replaced with a different material of the same thickness. This is done to increase the electric potential energy of the capacitor. Discuss why the capacitance also increases. Explain your reasoning by using the properties of capacitors, charge, electric potential, and energy.

• p:
Correct. Recognizes that the potential difference ΔV applied to the capacitor does not change (as it still connected to its emf source), uses at least one of two similar arguments:
1. because the electric potential energy is stated as increasing, then from EPE = (1/2)⋅Q⋅ΔV, then the charge Q in the capacitor must increase, and then from C = QV an increasing Q (with ΔV constant) means that the capacitance C must increase; or
2. from using EPE = (1/2)⋅C⋅(ΔV)2, increasing EPE with ΔV constant means that the capacitance C must increase.
• r:
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May not explicitly recognize that the potential difference ΔV applied to the capacitor is constant.
• 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 attempt at applying properties of capacitors, charge, electric potential, and energy.
• x:
Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of applying properties of capacitors, charge, electric potential, and energy.
• y:
Irrelevant discussion/effectively blank.
• z:
Blank.
Sections 30882, 30883
Exam code: midterm02Mc4s
p: 20 students
r: 7 students
t: 5 students
v: 10 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1104):

Another sample "p" response (from student 3214):