Physics midterm problem: unknown voltmeter reading

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 18.74

An ideal 15 V emf source is connected to ideal resistors and an ideal voltmeter, as shown at right. What is the reading of the voltmeter? Show your work and 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. From application of Kirchhoff's loop rule, voltmeter reading would be either 15 V - (6.0 Ω)·I₆, or (1.0 Ω)·I₁, or (5.0 Ω)·I₅, with I₆, I₁, and I₅ being the currents going through the 6.0 Ω resistor, 1.0 Ω light bulb, and 5.0 Ω resistor, respectively. Correctly finds one (or all) of the currents in this circuit by use of equivalent resistance, Ohm's law, and Kirchhoff's junction rule, and uses current(s) to determine the voltmeter reading.
  
• r:
  Nearly correct, but includes minor math errors.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least finds equivalent resistance of circuit, and main current I₆ = 2.2 A.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 31988
p: 4 students
r: 2 students
t: 3 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1230):