Physics final exam question: switching positions of ammeter and voltmeter

Physics 205B Final Exam, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 18.31, 18.41, 18.65

A 1.50 V emf battery with an unknown internal resistance r is connected to a light bulb of resistance R, and a voltmeter and an ammeter. All of these components are ideal. The internal resistance r is less than the resistance R of the light bulb. Discuss in which circuit (a) or (b) will the ammeter have a greater reading, or if there will be a tie. Explain your reasoning using the properties of voltmeters and ammeters, Kirchhoff's rules and Ohm's law.

Solution and grading rubric:
  • p:
    Correct. Understands that:
    1. a voltmeter has an infinite resistance, such that in circuit (a) it allows the current to flow through both the battery (with its internal resistance r) and the light bulb (of resistance R), while in circuit (b) the voltmeter prevents current from flowing through the light bulb, and only through the battery itself;
    2. from Ohm's law, the current flowing in circuit (a) is given by the emf of the battery divided by the sum of the resistances r and R, while in circuit (b) the current is given by the emf of the battery divided only the resistance r, such that the ammeter in (b) will have a higher reading than in the ammeter in (a).
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. One of the two points (1)-(2) correct, other is problematic/incomplete.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. Only one of the two points (1)-(2) correct, other is missing, or both are problematic.
  • 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:
Grading distribution:
Sections 30882, 30883
Exam code: finalLd0c
p: 12 students
r: 5 students
t: 4 students
v: 12 students
x: 10 students
y: 2 students
z: 1 student

A sample "p" response (from student 5425):

A sample "v" response (from student 0621):

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