Physics quiz question: equivalent resistance of circuit

Physics 205B Quiz 4, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 18.41(a)

Two ideal emf sources are connected to a 24 Ω resistor, and a 1.5 Ω light bulb, as shown at right. The equivalent resistance of this circuit is:
(A) 1.4 Ω.
(B) 10 Ω.
(C) 13 Ω.
(D) 26 Ω.

Correct answer (highlight to unhide): (A)

(The two ideal emf sources are in series with each other, but with opposite polarities, such that they can be replaced with an equivalent emf source of 12 V – 3.0 V = 9 V, in the same location and orientation as the 12 V emf source.)

The two resistors are in parallel with each other, such that their equivalent resistance is given by:

R_eq = (R₁^–1 + R₂^–1)^–1,

R_eq = ((24 Ω)^–1 + (1.5 Ω)^–1)^–1 = (0.70833333333 Ω^–1)^–1 = 1.4117647059 Ω,

or to two significant figures, the equivalent resistance of this circuit is 1.4 Ω.

(Response (B) is 1.4 Ω + 9.0 V; response (C) is the average of 24 Ω and 1.5 Ω; response (D) is 24 Ω + 1.5 Ω.)

Section 30882
Exam code: quiz04j0uL
(A) : 15 students
(B) : 1 student
(C) : 0 students
(D) : 10 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.70