Physics quiz question: resistance of unknown resistor in series circuit

Physics 205B Quiz 4, spring semester 2017
Cuesta College, San Luis Obispo, CA

Two different types of light bulbs, a resistor, and an ideal emf source are connected together. There is 0.32 A of current flowing through the emf. The resistance of the resistor is:
(A) 0.8 Ω.
(B) 2.1 Ω.
(C) 4.0 Ω.
(D) 4.7 Ω.

Correct answer: (C)

The resistor and the two light bulbs are in series with each other, such that their equivalent resistance is given by:

R_eq = R₁ + R₂ + R₃,

R_eq = R₁ + 0.50 Ω + 0.20 Ω.

The current flowing through this equivalent one emf, one resistor circuit is then given by Ohm's law:

I = ε/R_eq,

0.32 A = (1.5 V)/(R₁ + 0.50 Ω + 0.20 Ω),

which can be solved for the unknown resistance of the resistor:

R₁ + 0.70 Ω = (1.5 V)/(0.32 A),

R₁ = (1.5 V)/(0.32 A) – 0.70 Ω = 4.7 Ω – 0.70 Ω,

or to two significant figures, the resistance of the resistor is 4.0 Ω.

(Response (A) is 1.5 V – 0.70 Ω; response (B) is (1.5 V)/(0.70 Ω); response (D) is R_eq.)

Sections 30882, 30883
Exam code: quiz04Br7w
(A) : 2 students
(B) : 3 students
(C) : 11 students
(D) : 7 students

Success level: 48%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.34