Physics final exam problem: effect of removing light bulb from circuit

Physics 205B Final Exam, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Questions 18.22, 18.23, Problems 18.40, 18.41

Two identical light bulbs (R₁ = R₂ = 2.0 Ω), a third light bulb (r = 0.50 Ω), and an ideal 9.0 V emf source are connected as shown in the diagram at right. If the R₁ light bulb is completely removed from the circuit (and not replaced with anything, leaving that part of the circuit open), determine whether the brightness of the r light bulb would decrease, increase, or remain the same. Show your work and explain your reasoning.

Solution and grading rubric:

• p:
  Correct. Uses either a quantitative or qualitative argument to show that (1) the equivalent resistance is greater when the R₁ light bulb is disconnected from the circuit, resulting in (2) less current flowing through the r light bulb, (3) making it dissipate less power, and thus is dimmer.
• 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, 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:
  Blank.

Grading distribution:
Sections 30882
Exam code: finalpL3x
p: 3 students
r: 3 students
t: 8 students
v: 14 students
x: 0 students
y: 2 students
z: 0 students

A sample "p" response (from student 1224):
A sample "p" response (from student 1337):