Physics quiz question: US vs. European electricity

Physics 205B Quiz 5, Spring Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 18.113(d)

An 800 W room heater from Europe that plugs into a 240 V outlet is brought back home by a Physics 205B student, (somehow) plugging it into a 120 V outlet. How much power would the room heater use?
(A) 100 W.
(B) 200 W.
(C) 400 W.
(D) 680 W.

Correct answer: (B)

Assuming that the resistance of the heater remains constant, then the current used when plugged into a 120 V outlet is:

I_US = delta(V_US)/R = (120 V)/R = (1/2)*(240 V)/R = (1/2)*I_Europe.

Then the power used by heater when plugged into a 120 V outlet will be:

P_US = I_US*delta(V_US) = (1/2)*I_Europe*(1/2)*(V_Europe) = (1/4)*P_Europe = 200 W.

Response (A) is (1/8)*P_Europe; Response (C) is (1/2)*P_Europe; and response (D) is P_Europe - delta(V_US).

Student responses
Section 31988
(A) : 0 students
(B) : 0 students
(C) : 7 students
(D) : 3 students

Success level: 0%
Discrimination index (Aubrecht & Aubrecht, 1983): 0