Physics midterm question: unequal resistors in parallel

Physics 205B Midterm 2, fall semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 18.40(b)

An ideal emf source is connected in parallel to two resistors, where r < R. Determine which resistor has more current flowing through it, or if there is a tie. Explain your reasoning using the properties of currents and potential differences, and Kirchhoff's rules and Ohm's law.

Solution and grading rubric:

• p:
  Correct. Uses Ohm's law and the fact that each resistor has the same voltage drop (from inspection, or from explicit application of Kirchhoff's loop rule) to find that the resistor with the smaller resistance will have the greater current passing through it.
  
• 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.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 70856
p: 11 students
r: 0 students
t: 0 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7175):