20150517

Physics midterm problem: currents through each of two parallel bulbs

Physics 205B Midterm 2, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 18.40, 18.73, 18.75

An ideal emf source is connected to an ideal light bulb, and a certain amount of current (say, 0.40 A) flows through the bulb. A common misconception in analyzing circuits[*] is that if two of these bulbs (each with the same resistance as before) are connected in parallel to the same ideal emf, each of those bulbs would then get 0.20 A. Discuss why this is incorrect. Show your work and explain your reasoning using Kirchhoff's rules and Ohm's law.

[*] Dennis Albers, cited in Thomas O'Kuma, David P. Maloney, Curtis J. Hieggelke, Ranking Task Exercises in Physics, Prentice Hall (2000), p. 204.

Solution and grading rubric:
  • p:
    Correct. Discusses/demonstrates:
    1. that the parallel circuit light bulbs would still each have the same amount of current (0.40 A) as the lone light bulb attached to the same ideal emf source; or
    2. specifically argues why the parallel circuit light bulbs would not have one-half of the current of the lone light bulb attached to the same ideal emf source.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically solves for the equivalent resistance of the two light bulbs in parallel, and the total equivalent circuit current of 0.80 A, but only implicitly (if at all) mentions how each light bulb would divide up this current such that each does not get the incorrect 0.20 A value.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. At least understands equivalent resistance for light bulbs in parallel.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at discussing Kirchhoff's rules and Ohm's law.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. Approach other than that of discussing Kirchhoff's rules and Ohm's law.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 30882, 30883
Exam code: midterm02m3tR
p: 19 students
r: 13 students
t: 11 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1111), qualitatively appealing to Kirchhoff's loop rule:

A sample "p" response (from student 0196), quantitatively using specific numbers:

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