Physics midterm problem: comparing voltmeter readings

Physics 205B Midterm 2, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 18.72

Two voltmeters are connected to circuit with a switch, a light bulb, a resistor, and an emf source. All of these components are ideal. The resistance R of the resistor is greater than the resistance r of the light bulb. The top and bottom voltmeters have the same reading while the switch is open. Discuss why the top and bottom voltmeters will have different readings after the switch has been closed. Show your work and explain your reasoning using Kirchhoff's rules, Ohm's law, and properties of voltmeters.

Solution and grading rubric:

• p:
  Correct. Understands that closing the switch would allow current to flow through the emf, resistor and light bulb series circuit, while completely by-passing the lower voltmeter, such that:
  1. the upper voltmeter would read a non-zero voltage difference of ΔV = +ε – I∙R (or equivalently, ΔV = (–)I∙r); and
  2. the lower voltmeter would read zero, as there is no voltage drop due to the ideally zero resistance switch.
• r:
  Nearly correct, but includes minor math errors. Understands that current will now flow through the circuit, but does not give correct reading of one of the voltmeters, but has correct reading for the other.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Understands that current will now flow through the circuit, but does not give correct readings for both voltmeters.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. At least understands that current will now flow through the circuit.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Kirchhoff's rules, Ohm's law, and properties of voltmeters.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: midterm02m3tR
p: 8 students
r: 15 students
t: 7 students
v: 14 students
x: 3 students
y: 0 students
z: 0 students

A sample "p" response (from student 9178):