Physics midterm problem: Christmas light bulb circuit

Physics 205B Midterm 2, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Questions 18.21-18.23, Multiple-Choice Question 18.9, Problem 18.65(e)

Two identical light bulbs[*] (R₁ = R₂ = 3.0 Ω), and two identical resistors[**] (r₁ = r₂ = 500 Ω) are wired such that each bulb is in parallel with a resistor, and these bulb-resistor sets are in series with an ideal 2.2 V emf source. Determine (a) the potential difference across the R₂ light bulb while both R₁ and R₂ bulbs are on, and (b) the potential difference across the R₂ light bulb after the R₁ light bulb burns out[***] (effectively leaving a gap in its place). Show your work and explain your reasoning.

[*] http://www.christmaslightsetc.com/p/100-Clear-Mini-Christmas-Lights-4-inch-Spacing-Green-Wire--15199.htm.
[**] U.S Patent no. 6,323,597, "Thermistor shunt for series wired light string," https://www.google.com/patents/US6323597.
[**] This simplification ignores the drop in shunt resistance with increasing temperature after the light bulb filament burns out, http://people.howstuffworks.com/culture-traditions/holidays-christmas/christmas-lights1.htm.

Solution and grading rubric:

• p:
  Correct. Applies equivalent resistance and Ohm's law to determine the current flowing through the equivalent circuits (a) and (b), and uses Kirchhoff's loop rule to find the voltage drop through the second light bulb in circuits (a) and (b).
• r:
  Nearly correct, but includes minor math errors. May have solved for the drop across the r₁ resistor instead of across the R₂ light bulb in circuit (b).
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has the voltage drop across the R₂ light bulb in circuit (a).
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at using Kirchhoff's rules, Ohm's law, and equivalent resistance.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: midterm02iF47
p: 18 students
r: 5 students
t: 3 students
v: 11 students
x: 2 students
y: 1 student
z: 0 students

A sample "p" response (from student 3724):