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:
R2,4 = [ (R2)–1 + (R4)–1 ]–1,
R2,4 = [ (2.0 Ω)–1 + (4.0 Ω)–1 ]–1,
R2,4 = 1.333... Ω.
Then the 8.0 Ω resistor is in series with the combined R2,4 equivalent resistor, so the final equivalent resistance of the circuit is:
Req = R8 + R2,4,
Req = 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 R2,4 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
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