## 20140511

### Physics midterm problem: placing meters between batteries

Physics 205B Midterm 2, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 18.31, 18.72, 18.73

Two nickel-metal hydride (NiMH) batteries[*] each with an emf of 1.2 volts and an internal resistance of 0.1 Ω are connected to a 16.0 Ω light bulb[**], with an open gap between the batteries. In this gap, either an ideal voltmeter, or an ideal ammeter is to be connected. Determine (a) the voltmeter reading when it is connected between the batteries, and (b) the ammeter reading when it is connected between the batteries. Show your work and explain your reasoning using the properties of currents and potential differences, and Kirchhoff's rules and Ohm's law.

[*] "Cell charged: 100 milliohms," ti.com/lit/an/slva194/slva194.pdf.
[**] goo.gl/jLtakj.

Solution and grading rubric:
• p:
Correct. Applies Kirchhoff's loop rule and the fact that no current would flow through circuit (a) due to the infinite resistance of the ideal voltmeter to determine that should read 2.4 V; applies equivalent resistance and Ohm's law to determine the current flowing through the ideal (zero resistance) ammeter in circuit (b) should be 0.15 A.
• r:
Nearly correct, but includes minor math errors.
• t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Voltmeter reading in circuit (a) is zero ("no current flow" = no voltage differences), infinite ("no current flow" = infinite/undefined voltage differences), or some value slightly less than 2.4 V due to internal resistance voltage drops (which would only be true if current were flowing through them), but still has the correct ammeter reading for circuit (b).
• v:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at using Kirchhoff's rules, Ohm's law, and equivalent resistance.
• x:
Implementation of ideas, but credit given for effort rather than merit.
• y:
Irrelevant discussion/effectively blank.
• z:
Blank.
Sections 30882, 30883
Exam code: midterm02iF47
p: 3 students
r: 2 students
t: 23 students
v: 10 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 7979):