## 20160508

### Physics midterm question: equally bright, different resistance light bulbs

Physics 205B Midterm 2, spring 2016
Cuesta College, San Luis Obispo, CA

An 6.0 V emf source is connected to a resistor r, and two light bulbs with different resistances R1 and R2. Both light bulbs have the same brightness. Discuss why R1 > R2. Explain your reasoning using Kirchhoff's rules, Ohm's law, and electric power.

Solution and grading rubric:
• p:
Correct. Discusses/demonstrates how R1 > R2 using at least one of two similar arguments:
1. the current that flows through the R2 light bulb and emf splits in parallel through both the resistor and the R1 light bulb, such that I2 is greater than I1, and given P1 = P2, then (I1)2R1 = (I2)2R2, and since I2 is greater than I1, then R2 must be less than R1; or
2. the current that flows through the R2 light bulb and emf splits in parallel through both the resistor and the R1 light bulb, such that I2 is greater than I1, and given P1 = P2, then I1⋅ΔV1 = I2⋅ΔV2, and since I2 is greater than I1, then ΔV2 is less than ΔV1, such that I2R2 is less than I1R1, and again from I2 is greater than I1, thus R2 must be less than R1.
• r:
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
Nearly correct, but argument has conceptual errors, or is incomplete. May use the statement to be proved (R1 > R2) and given information (P1 = P2) to instead demonstrate how I2 is greater than I1 and/or ΔV2 is less than ΔV1; or does not sufficiently show how either I2 is greater than I1 and/or ΔV2 is less than ΔV1 in order to prove that R1 > R2.
• 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.
• 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.

Sections 30882, 30883
Exam code: midterm02Mc4s
p: 8 students
r: 4 students
t: 11 students
v: 15 students
x: 4 students
y: 0 students
z: 0 students

A sample "p" response (from student 1157):