Physics final exam problem: parallel versus series brightnesses

Physics 205B Final Exam, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 18.107

Two circuits are constructed using identical, ideal 9.0 V batteries, and two lightbulbs of different resistances r and R. The light bulbs of resistances r and R in the parallel circuit dissipates 12.0 W and 8.0 W of power, respectively. In the series circuit, determine (a) how much power the light bulb of resistance r dissipates, and (b) how much power the light bulb of resistance R dissipates. Ignore changes in the resistances of the bulbs due to temperature changes. Show your work and explain your reasoning using the properties of currents and potential differences, and Kirchhoff's rules and Ohm's law.

Solution and grading rubric:
  • p:
    Correct. Recognizes that the light bulbs in parallel both use the whole 9.0 V of the emf, and solves for the resistances r and R. Finds the equivalent resistance of the series circuit, in order to solve for the current that both light bulbs use when in series. Then finds the powers used by the light bulbs in series.
  • r:
    Nearly correct, but includes minor math errors.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Only one step in (p) correct: typically finding the resistances r and R.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Problematic application of equivalent resistance rules, Ohm's law, and Kirchhoff's rules.
  • x:
    Implementation of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:

Grading distribution:
Section 30882
Exam code: finalsM0k
p: 7 students
r: 0 students
t: 9 students
v: 7 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 6969):
A much more exhaustive sample "p" response (from student 1203):

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