Physics midterm question: effect of shunting a light bulb

Physics 205B Midterm 2, spring semester 2017
Cuesta College, San Luis Obispo, CA

An ideal 6.0 emf source is connected to a switch, resistor, and two light bulbs. While the switch is open, the two light bulbs have the same brightness. Discuss why one light bulb will be brighter than the other after the switch is closed. Explain your reasoning using Kirchhoff's rules, Ohm's law, and properties of electric power.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates how the light bulbs will have a different brightness (more specifically, the top light bulb will be brighter than the lower light bulb) when the switch is closed because:
  1. when the switch is open, the same current flows through both the top and the bottom light bulb, and because they have the same brightness, they must have the same resistance, from:
     
     I₁ = I₂ (in series),
     
     and P₁ = P₂ (same brightness), then:
     
     (I₁)²⋅R₁ = (I₂)²⋅R₂,
     
     ∴ R₁ = R₂; and
     
     
  2. when the switch is closed, from Kirchhoff's junction rule the current that flows through the top light bulb must split between going through the bottom light bulb and through the resistor. Because the current flowing through the bottom light bulb must be less than the current that flows through the top light bulb (and since they have the same resistance), then they will have different brightnesses (the top light bulb will be brighter than the bottom light bulb:
     
     I₁ = I₂ + I_resistor (Kirchhoff's junction rule), then:
     
     I₁ > I₂, and:
     
     R₁ = R₂ (from before), such that:
     
     (I₁)²⋅R₁ > (I₂)²⋅R₂, making P₁ > P₂.
     
  
  
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May not have deduced that the light bulbs must have the same resistance (otherwise argument (2) based on difference in currents alone would not necessarily be true).
  
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. May not have explicitly used power equations to show how current and resistance support argument.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some attempt at applying properties of Kirchhoff's rules, Ohm's law, and electric power. At least recognizes that current is split when the switch is closed.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of applying Kirchhoff's rules, Ohm's law, and electric power.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm02GruT
p: 9 students
r: 7 students
t: 10 students
v: 2 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 8108):