Physics final exam problem: ranking light bulb brightnesses

Physics 205B Final Exam, spring semester 2014
Cuesta College, San Luis Obispo, CA

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

Two identical light bulbs (R1 = R2 = 5.0 Ω), a third light bulb (r = 1.0 Ω), and an ideal 15 V emf source are connected as shown in the diagram at right. Rank the brightness of these light bulbs, from dimmest to brightest. Indicate ties, if any. Show you work and explain your reasoning using Kirchhoff's rules, Ohm's law, and electric power.

Solution and grading rubric:
  • p:
    Correct. Uses either a (1) quantitative or (2) qualitative argument to rank the light bulbs in increasing brightness: P2 < Pr < P1.
    1. Finds (a) the equivalent resistance of the circuit to determine (b) the current flowing through R1 (and the power P1), (c) applies Kirchhoff's loop rule to determine the voltage used by R1 to determine the voltage used by either r or R2 which can be used to find Pr and P2.
    2. Discusses how (a) P2 < P1 because due to Kirchhoff's junction rule, bulb R1 will have more current than bulb R2, and as they have the same resistance, from P = I2·R, P2 < P1; and (b) similarly bulb r will have less current than bulb R1, and with less resistance than R1, Pr < P1; and (c) from Kirchhoff's loop rule, r and R2 will have the same potential difference ΔV, and since r < R1, then from P = (ΔV)2/R, Pr > P_2, such that P2 < Pr < P1.
  • r:
    Nearly correct, but includes minor math errors.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Problematic application of equivalent resistance, Ohm's law (and/or Kirchhoff's circuit rules), and power.
  • x:
    Implementation of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 30882, 30883
Exam code: finalEL7a
p: 10 students
r: 7 students
t: 11 students
v: 7 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student):

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