Physics final exam question: voltmeter reading of leaking capacitor

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

A capacitor is made from two parallel metal plates, and is charged with equal amounts of opposite charge. Both capacitor plates slowly lose their charge, due to being exposed to humid air. Discuss why the voltmeter reading attached to the capacitor decreases as this happens. Explain your reasoning by using the properties of capacitors, charge, electric potential, and energy.

Solution and grading rubric:

• p:
  Correct. Explains why the voltmeter reading will decrease as the capacitor plates lose their charge, by discussing:
  1. that the capacitance must remain constant, as the plate area and the spacing between the plates remain constant; and
  2. because capacitance remains constant, then charge and voltage difference are proportional to each other, and thus a decrease in charge results in a decrease in voltage difference.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Does not explicitly discuss (1).
• 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 garbled attempt at applying the properties of capacitors, charge, electric potential, and energy.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying the properties of capacitors, charge, electric potential, and energy.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 7 students
r: 8 students
t: 1 student
v: 5 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 4447):

Physics final exam question: induced current in loops surrounding vertical wire

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


A vertical wire has a decreasing amount of current flowing upwards. Circular metal loops (of resistance R) oriented flat along the north-south direction are held by four different observers. Determine which observer (if any) will have a coil with an induced counterclockwise current, as seen in this perspective. Explain your reasoning using the properties of magnetic fields, forces, motional emf, Faraday's law and Lenz's law.

Solution and grading rubric:

• p:
  Correct. Determines that only the north observer will experience a counterclockwise induced current, by discussing:
  1. right-hand rule 2, where the thumb runs along a straight current-carrying wire, and fingers curled around the wire give the direction of the magnetic field surrounding the wire; and
  2. from Faraday's law, the east and west observers have coils that will not receive any magnetic flux from the wire's current, so they will not observe any induced current in their coils; while the north and south observers have coils that are oriented to receive the changing magnetic flux from the wire's decreasing current, so they will observe an induced current in their coils; and
  3. from Lenz's law (and right-hand rule 3), only the north observer will experience a counterclockwise induced current to counter the decreasing flux that points east-to-west through it (while the south observer will experience a clockwise induced current to counter the decreasing flux that points west-to-east 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. Correctly discusses (1)-(2), but has problems with discussing (3): typically may not have explicitly discussed why the magnetic field of the induced current in the north observer's loop must point in the same direction as the (decreasing) magnetic field from the wire, or determines that the south observer's coil will have a counterclockwise induced current.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least some attempt at using magnetic forces and/or magnetic flux. Correctly discusses (1)-(2), but discussion of (3) is incomplete or missing.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying theproperties of magnetic fields, forces, motional emf, Faraday's law and Lenz's law.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying the properties of magnetic fields, forces, motional emf, Faraday's law and Lenz's law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 1 student
r: 11 students
t: 2 students
v: 11 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 7117):

Physics final exam question: valid or invalid Feynman diagram?

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

Discuss whether this Feynman diagram is valid or invalid. Explain your reasoning using the properties of Feynman diagrams, particles and antiparticles, and interactions.

Solution and grading rubric:

• p:
  Correct. Argues why this Feynman diagram is invalid by either one of two arguments:
  1. this process is not a proper permutation of a known weak interaction (as the nucleon changes into a lepton in the top path); or
  2. charge conservation is violated (zero charge of neutron does not equal the net positive charge of neutrino, positron, and proton out).
• 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. May argue why this Feynman diagram is invalid as does not correspond to a known weak decay process (but discussion of the known weak decay process is garbled); or argues that this Feynman diagram is valid as the "one line in, one line out" vertex rule is obeyed by both vertices (although charge conservation is violated, and the nucleon and lepton paths are mixed).
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying properties of Feynman diagrams, particles and antiparticles, and interactions.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying properties of Feynman diagrams, particles and antiparticles, and interactions.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 3 students
r: 3 students
t: 18 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7117):

Physics final exam problem: microscope object distance

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

A NASA education guide for high school students[*] details plans for a simple microscope using an f = +28 mm objective lens and an f = +46 mm eyepiece lens, separated by a lens-to-lens distance of 160 mm. Determine the distance (in mm) that an object should be placed at in front of the objective lens for viewing through this microscope. Show your work and explain your reasoning by using ray tracings and/or thin lens equations, properties of lenses, images, and magnification.

[*] nasa.gov/pdf/350502main_Optics_Building_a_Microscope.pdf.

Solution and grading rubric:

• p:
  Correct. Determines the object distance d_o1 for the objective lens by discussing:
  1. that the lens-to-lens distance is equal to the objective image distance d_i1 plus the eyepiece focal length f₂ (as the image produced by the objective is placed at the focal point of the eyepiece), such that d_i1 = 160 mm − 46 mm = 114 mm; and
  2. knowing the focal point f₁ = +28 mm and the image distance d_i1 = 114 mm for the objective lens, uses the thin lens equation to find the object distance d_o1 for the objective lens.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least recognizes the placement of the intermediate image produced by the objective lens between the objective lens and eyepiece lens.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Garbled attempt at applying ray tracings and/or thin lens equations, properties of lenses, images, and magnification.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying ray tracings and/or thin lens equations, properties of lenses, images, and magnification.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 1 student
r: 1 student
t: 5 students
v: 14 students
x: 3 students
y: 1 student
z: 1 student

A sample "p" response (from student 7117):

Physics final exam problem: destructive interference angles in one quadrant

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

Two vertical radio transmitters broadcast in phase at the same wavelength of 1.2 m, and are spaced a certain apart along the east-west direction. A Physics 205B student holding a receiver starts from due south of the transmitters, and detects three different locations with destructive interference signals before finally reaching due east of the transmitters. Determine a plausible separation distance (in m) between the transmitters. Explain your reasoning using the properties of source phases, path lengths, and interference.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates that three minima locations will be found in the range θ = 0° (due south) to 90° (due west) by using one of two approaches:
  1. using the destructive interference condition d⋅sinθ = (m + 1/2)⋅λ, where m = 0, 1, 2, ..., finds a plausible separation distance d such that the third minima (m = 2) will be within θ = 90°, but the fourth minima (m = 3) is outside of θ = 90° (i.e., 3.0 m ≤ d ≤ 4.8 m); or
  2. using the constructive interference condition d⋅sinθ = m⋅λ, where m = 0, 1, 2, ..., finds the separation distance d such that the third maxima (m = 3) will be at θ = 90°; which allows for the m = 0, 1, and 2 minima to exist within that range (i.e., d = 3.6 m).
• r:
  Nearly correct, but includes minor math errors. May have claimed equally spaced minima angles at θ = 30°, 60° and 90° to find a plausible separation distance d using θ = 30° for the first minima angle.
• 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. Garbled attempt at applying properties of source phases, path lengths, and interference.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying properties of source phases, path lengths, and interference.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 3 students
r: 4 students
t: 6 students
v: 7 students
x: 4 students
y: 2 students
z: 0 students

A sample "p" response (from student 0428), finding the maximum possible separation distance:

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):