Physics midterm question: comparing voltmeter readings

Physics 205B Midterm 2, spring semester 2019
Cuesta College, San Luis Obispo, CA

An ideal 9.0 V emf source is connected to a light bulb and two resistors, with a voltmeter connected to the light bulb, and another voltmeter connected to one of the resistors. Discuss why the two voltmeters have the same reading (in volts). Show your work and explain your reasoning using Kirchhoff's laws, Ohm's law, and properties of voltmeters.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates how the two voltmeters have the same reading because:
  1. due to Kirchhoff's junction rule, the current flowing through each of the 4.0 Ω resistors is one-half of the current flowing through the 2.0 Ω resistor; and
  2. since each voltmeter will read the voltage drop (I⋅R) of their respective resistors, the smaller current (factor of one-half) flowing through the 4.0 Ω resistor will be compensated by its larger resistance (factor of two).
• 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. Some attempt at applying properties of Kirchhoff's rules, Ohm's law, and properties of ammeters.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at systematically applying Kirchhoff's rules, Ohm's law, and properties of ammeters.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: midterm02u7aH
p: 28 students
r: 4 students
t: 2 students
v: 8 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 1950):

Physics midterm question: ammeter reading after switch is closed

Physics 205B Midterm, spring semester 2019
Cuesta College, San Luis Obispo, CA

An ideal 6.0 V emf source is connected to an ammeter, a resistor, a light bulb, and an open switch. When the switch is closed, determine whether the ammeter reading (in amps) will decrease, increase, or remain the same, and explain why. 
Show your work and explain your reasoning using Kirchhoff's rules, Ohm's law, and properties of ammeters.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates how ammeter reading will increase when the switch is closed because:
  1. when the switch is open, the equivalent resistance is 3.0 Ω, and the ammeter will read the current of this circuit I = ε_eq/R_eq = (6.0 V)/(3.0 Ω) = 2.0 A;
  2. when the switch is closed, no current will flow through the 0.5 Ω resistor (flowing only through the zero resistance path of the closed switch), such that the equivalent resistance decreases to 2.5 Ω, such that the ammeter will read a higher amount of current in this circuit I = ε_eq/R_eq = (6.0 V)/(2.5 Ω) = 2.4 A.
• 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. Some attempt at applying properties of Kirchhoff's rules, Ohm's law, and properties of ammeters.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at systematically applying Kirchhoff's rules, Ohm's law, and properties of ammeters.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: midterm02u7aH
p: 20 students
r: 4 students
t: 10 students
v: 6 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1001):
Another sample "p" response (from student 1810):

Physics final exam problem: ammeter and voltmeter readings

Physics 205B Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA

A lithium battery with an emf of 3.6 V and an internal resistance of r = 0.45 Ω is connected to two light bulbs (each with different resistances), an ammeter, and a voltmeter. Determine (a) the ammeter reading (in amps) and (b) the voltmeter reading (in volts). Show your work and explain your reasoning using the properties of voltmeters, Kirchhoff's rules and Ohm's law.

Solution and grading rubric:

• p:
  Correct. Determines the ammeter and voltmeter readings by:
  1. finding the equivalent resistance of the circuit, and then uses Ohm's law to determine the current passing through the 0.45 Ω resistor; and
  2. knowing the current and the resistance, uses Ohm's law to determine the drop in voltage across the 0.45 Ω resistor; and
  3. knowing the voltage rise of the emf and the voltage drop across the 0.45 Ω resistor, uses Kirchhoff's loop rule and Ohm's law to determine the current passing through the 1.2 Ω resistor, which is the ammeter reading; then
  4. knowing the voltage rise of the emf and the voltage drop across the 0.45 Ω resistor, uses Kirchoff's loop rule to determine the voltage drop across the 2.2 Ω resistor, which is the voltmeter reading.
• r:
  Nearly correct, but includes minor math errors. Has determined at least one of (1)-(2), but only one of (3)-(4) is complete/correct.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least only one of (1)-(2) is complete/correct.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Garbled attempt at applying Kirchhoff's rules, Ohm's law, and properties of ammeters.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying Kirchhoff's rules, Ohm's law, and properties of ammeters.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 2 students
r: 2 students
t: 4 students
v: 2 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student):

Physics midterm problem: pencil lead variable resistor

Physics 205B Midterm 2, spring semester 2017
Cuesta College, San Luis Obispo, CA

A real battery with an emf of 6.0 V and an internal resistance of r = 1.2 Ω is attached to an ideal voltmeter, and is connected to an ideal ammeter and a pencil lead that acts as a variable resistor. If the amount of pencil lead between the contacts is shortened such that its resistance is reduced from 8.0 Ω to 1.0 Ω, discuss why the voltmeter reading will decrease while the ammeter reading will increase. Show your work and explain your reasoning using Kirchhoff's rules, Ohm's law, and properties of ammeters and voltmeters.

Solution and grading rubric:

• p:
  Correct. Explains why the voltmeter reading will decrease while the ammeter reading will increase as the amount of pencil lead between the contacts is shortened by discussing:
  1. the decrease in the resistance of the pencil lead resistor will reduce the equivalent resistance of the circuit (pencil lead and internal resistance are in series), such that from applying Ohm's law the amount of current passing everywhere through the circuit will increase, resulting in a higher ammeter reading; and
  2. the voltmeter measures the potential difference of the 6.0 V rise from the emf and the voltage drop I⋅r from the internal resistance, such that an increase in current will result in a lower voltage reading ΔV = +ε − I⋅r.
(May instead discuss how the voltmeter is equivalently measuring the voltage drop ΔV = −I⋅R across the pencil lead resistor, but must clearly show that the eight-fold decrease in the resistance (from 8.0 Ω to 1.0 Ω) will be larger than the corresponding approximate four-fold increase in current (0.65 A to 2.7 A) to result in a lower voltage 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 numerically or qualitatively demonstrates how current would increase, but does not definitely show why voltmeter reading would decrease.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at applying Kirchhoff's rules, Ohm's law, and equivalent resistance.
• 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 ammeters and voltmeters.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: midterm02GruT
p: 12 students
r: 0 students
t: 8 students
v: 8 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1412):
Another sample "p" response (from student 2643):
A sample "x" response (from student 9319):

Physics final exam problem: shunted voltmeter readings

Physics 205B Final Exam, spring semester 2016
Cuesta College, San Luis Obispo, CA


A 4.5 V emf source is connected to two light bulbs (each with different resistances), two voltmeters, and a switch. All of these components are ideal. Discuss why the voltmeters have equal readings while the switch is closed, and have unequal readings after the switch is opened. Show your work and explain your reasoning using the properties of voltmeters, Kirchhoff's rules and Ohm's law.

Solution and grading rubric:

• p:
  Correct. Explicitly explains/demonstrates that the voltmeters in the closed-switch circuit have equal readings, and the voltmeters in the open-switch circuit have unequal readings by:
  1. applying Kirchhoff's loop rule to both circuits; and/or
  2. explicitly calculating the voltage drops for each of the voltmeters in both circuits.
• r:
  Nearly correct, but includes minor math errors. For the closed-switch circuit, may instead compare the different amount of currents flowing through each light bulb, instead of through each ammeter.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
• 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. No clear attempt at 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: finalm4u1
p: 11 students
r: 8 students
t: 7 students
v: 7 students
x: 4 students
y: 0 students
z: 2 students

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

Physics final exam problem: shunted ammeter readings

Physics 205B Final Exam, spring semester 2016
Cuesta College, San Luis Obispo, CA


A 4.5 V emf source is connected to two light bulbs (each with different resistances), two ammeters, and a switch. All of these components are ideal. Discuss why the ammeters have unequal readings while the switch is closed, and have equal readings after the switch is opened. Show your work and explain your reasoning using the properties of ammeters, Kirchhoff's rules and Ohm's law.

Solution and grading rubric:

• p:
  Correct. Explicitly explains/demonstrates that the ammeters in the closed-switch circuit have unequal readings, and the ammeters in the open-switch circuit have equal readings by:
  1. applying Kirchhoff's junction rule to both circuits; and/or
  2. explicitly calculating the currents that flow through each of the ammeters in both circuits.
• r:
  Nearly correct, but includes minor math errors. For the closed-switch circuit, may instead compare the different amount of currents flowing through each light bulb, instead of through each ammeter.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying Kirchhoff's rules, Ohm's law, and properties of ammeters.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: finalm4u1
p: 12 students
r: 14 students
t: 5 students
v: 3 students
x: 2 students
y: 2 students
z: 1 student

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

Physics midterm problem: change in voltmeter reading

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

A "AA" alkaline battery with an emf of 1.5 V and an internal resistance of r = 0.90 Ω is attached to an ideal voltmeter, with a R = 2.0 Ω light bulb that is wired in parallel with an open switch. Discuss why the voltmeter will have a lower reading after the switch is 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. Recognizes that when the switch is open, the voltmeter will have a non-zero reading, and have a lower (zero) reading when the switch is closed, using one of two similar arguments:
  1. when the switch is open, there is a non-zero ΔV = +1.5 V − I⋅r reading, and when the switch is closed, from Kirchhoff's loop rule the voltage rise of +1.5 V from the emf must now exactly equal the −I⋅r voltage drop of the internal resistance of the battery, such that the voltmeter reading is now zero; or
  2. when the switch is open, there is a non-zero ΔV = − I⋅R reading, and when the switch is closed, since the light bulb R is bypassed by a zero resistance switch, making ΔV = 0.
• r:
  Nearly correct, but includes minor math errors. Does not sufficiently show numerically or qualitatively how voltmeter reading when switch is open is higher versus when the switch is closed.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has a conceptual understanding of how a voltmeter measures a potential difference, and how the switch changes the current flow when it is open versus when it is closed.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at applying Kirchhoff's rules, Ohm's law, and equivalent resistance.
• 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: midterm02Mc4s
p: 7 students
r: 17 students
t: 4 students
v: 12 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 3158):
Another sample "p" response (from student 5433):

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):

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.

Grading distribution:
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):

Physics midterm problem: Christmas light bulb circuit

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Questions 18.21-18.23, Multiple-Choice Question 18.9, Problem 18.65(e)

Two identical light bulbs[*] (R₁ = R₂ = 3.0 Ω), and two identical resistors[**] (r₁ = r₂ = 500 Ω) are wired such that each bulb is in parallel with a resistor, and these bulb-resistor sets are in series with an ideal 2.2 V emf source. Determine (a) the potential difference across the R₂ light bulb while both R₁ and R₂ bulbs are on, and (b) the potential difference across the R₂ light bulb after the R₁ light bulb burns out[***] (effectively leaving a gap in its place). Show your work and explain your reasoning.

[*] http://www.christmaslightsetc.com/p/100-Clear-Mini-Christmas-Lights-4-inch-Spacing-Green-Wire--15199.htm.
[**] U.S Patent no. 6,323,597, "Thermistor shunt for series wired light string," https://www.google.com/patents/US6323597.
[**] This simplification ignores the drop in shunt resistance with increasing temperature after the light bulb filament burns out, http://people.howstuffworks.com/culture-traditions/holidays-christmas/christmas-lights1.htm.

Solution and grading rubric:

• p:
  Correct. Applies equivalent resistance and Ohm's law to determine the current flowing through the equivalent circuits (a) and (b), and uses Kirchhoff's loop rule to find the voltage drop through the second light bulb in circuits (a) and (b).
• r:
  Nearly correct, but includes minor math errors. May have solved for the drop across the r₁ resistor instead of across the R₂ light bulb in circuit (b).
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has the voltage drop across the R₂ light bulb in circuit (a).
• 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.

Grading distribution:
Sections 30882, 30883
Exam code: midterm02iF47
p: 18 students
r: 5 students
t: 3 students
v: 11 students
x: 2 students
y: 1 student
z: 0 students

A sample "p" response (from student 3724):