## 20170409

### Physics quiz question: comparing potential differences for parallel resistors

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

A light bulb and a resistor are connected to two ideal emf sources. The __________ has a greater potential difference.
(A) light bulb.
(B) resistor.
(C) (There is a tie.)
(D) (Not enough information is given.)

(The two emf sources are in series with each other, such that the equivalent emf in this circuit is 9.0 V + 3.0 V = 12.0 V.)

The resistor and the light bulb are in parallel with each other, and can be analyzed separately using Kirchhoff's loop rule. Applying the loop rule in the counterclockwise direction, starting from lower left-hand corner, through the 3.0 V emf source, through the 15 Ω resistor, and through the 9.0 V emf source before returning to the starting point in the lower left-hand corner results in:

0 = +3.0 V – Iresistor·R + 9.0 V,

where the sum of these potential rises and drop is set equal to zero for this (or any) complete loop around a circuit.

Similarly, applying the loop rule in the counterclockwise direction, starting from lower left-hand corner, through the 3.0 V emf source, through the 1/3 Ω light bulb, and through the 9.0 V emf source before returning to the starting point in the lower left-hand corner results in:

0 = +3.0 V – Ilight bulb·r + 9.0 V,

where again the sum of these potential rises and drop is set equal to zero for this (or any) complete loop around a circuit.

From inspection, the potential drop across the resistor Iresistor·R is 12.0 V, and the potential drop across the light bulb Ilight bulb·r is also 12.0 V, meaning they have the same drop in potential (but different amounts of currents), as is typical for any two resistive circuit elements in parallel with each other.

Sections 30882, 30883
Exam code: quiz04Br7w
(A) : 4 students
(B) : 16 students
(C) : 3 students
(D) : 0 students

Success level: 13%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.25