Physics midterm question: 240 V light bulb in 120 V socket

Physics 205B Midterm 2, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 22.45

A question on an online discussion board[*] was asked and answered:

Would a 25 W light bulb (for a 240 V socket) be dimmer in a 120 V socket?
Yes, but you get a lot less than half the light, even though the applied voltage is half the rated voltage.

Discuss why this answer is correct, and how you know this. Explain your reasoning using the properties of currents and potential differences, and Kirchhoff's rules and Ohm's law.

[*] wiki.answers.com/Q/Can_a_240V_lightbulb_25W_work_in_a_120V_socket_and_would_it_just_be_dimmer.

Solution and grading rubric:

• p:
  Correct. Applies Ohm's law and/or power equations, keeping the resistance the same to determine that the light bulb in the 120 V socket would use one-quarter of the power in the 240 V socket.
• 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. Finds different resistances for light bulb, based on power being the same in either socket.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882
Exam code: midterm02w1Ig
p: 8 students
r: 3 students
t: 6 students
v: 16 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1029):