Physics quiz question: equivalent resistance of serio-parallel circuit

Physics 205B Quiz 5, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 18.112

An ideal 12 V emf source is connected to three resistors, as shown at right. The equivalent resistance of this circuit 
is:
(A) 3.4 Ω.
(B) 4.7 Ω.
(C) 9.3 Ω.
(D) 14.0 Ω.

Correct answer: (C)

The 2.0 Ω resistor and the 4.0 Ω resistor are directly connected in parallel to each other, such that their equivalent resistance is:

R_2,4 = [ (R₂)^–1 + (R₄)^–1 ]^–1,

R_2,4 = [ (2.0 Ω)^–1 + (4.0 Ω)^–1 ]^–1,

R_2,4 = 1.333... Ω.

Then the 8.0 Ω resistor is in series with the combined R_2,4 equivalent resistor, so the final equivalent resistance of the circuit is:

R_eq = R₈ + R_2,4,

R_eq = 8.0 Ω + 1.333... Ω = 9.3 Ω, to the significant tenths decimal place.

(Response (A) is where the 2.0 Ω resistor and the 4.0 Ω resistor are first combined in series, and their resulting equivalent resistance R_2,4 combined in parallel with the 8.0 Ω resistor; response (B) is the average of all three resistance values; response (D) is the sum of all three resistance values.)

Section 30882
Exam code: quiz04eQu7
(A) : 1 student
(B) : 4 students
(C) : 25 students
(D) : 2 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38