Cuesta College, San Luis Obispo, CA
A "AA" alkaline battery with an emf of 1.5 V and an internal resistance of r = 0.90 Ω is attached to an ideal voltmeter, with a R = 2.0 Ω light bulb that is wired in parallel with an open switch. Discuss why the voltmeter will have a lower reading after the switch is closed. Show your work and explain your reasoning using Kirchhoff's rules, Ohm's law, and properties of voltmeters.
Solution and grading rubric:
Correct. Recognizes that when the switch is open, the voltmeter will have a non-zero reading, and have a lower (zero) reading when the switch is closed, using one of two similar arguments:
- when the switch is open, there is a non-zero ΔV = +1.5 V − I⋅r reading, and when the switch is closed, from Kirchhoff's loop rule the voltage rise of +1.5 V from the emf must now exactly equal the −I⋅r voltage drop of the internal resistance of the battery, such that the voltmeter reading is now zero; or
- when the switch is open, there is a non-zero ΔV = − I⋅R reading, and when the switch is closed, since the light bulb R is bypassed by a zero resistance switch, making ΔV = 0.
Nearly correct, but includes minor math errors. Does not sufficiently show numerically or qualitatively how voltmeter reading when switch is open is higher versus when the switch is closed.
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has a conceptual understanding of how a voltmeter measures a potential difference, and how the switch changes the current flow when it is open versus when it is closed.
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at applying Kirchhoff's rules, Ohm's law, and equivalent resistance.
Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Kirchhoff's rules, Ohm's law, and properties of voltmeters.
Irrelevant discussion/effectively blank.
Sections 30882, 30883
Exam code: midterm02Mc4s
p: 7 students
r: 17 students
t: 4 students
v: 12 students
x: 2 students
y: 0 students
z: 0 students
A sample "p" response (from student 3158):
Another sample "p" response (from student 5433):