Physics quiz question: power dissipated by resistor in parallel circuit

Physics 205B Quiz 5, spring semester 2018
Cuesta College, San Luis Obispo, CA

An ideal 6.0 V emf source is connected to a resistor and two light bulbs. The electrical power used by the 4.0 Ω resistor is:
(A) 1.5 W.
(B) 9.0 W.
(C) 24 W.
(D) 96 W.

Correct answer (highlight to unhide): (B)

The basic equation for the power dissipated by the 4.0 Ω resistor is:

P_resistor = I_resistor·ΔV_resistor,

where the current through the resistor I_resistor is not equal to the current passing through the 6.0 V emf source (I_circuit = ΔV_resistor/R_eq), due to the junction rule. However, we do not need to find I_resistor, as we can appeal to Ohm's law:

I_resistor = ΔV_resistor/R_resistor,

such that we can substitute this into the basic power equation, and result in a "specialized" form of the power equation for this resistor:

P_resistor = I_resistor·ΔV_resistor,

P_resistor = (ΔV_resistor/R_resistor)·ΔV_resistor,

P_resistor = (ΔV_resistor)²/R_resistor.

To find the ΔV_resistor voltage used by the resistor, we apply the loop rule in the clockwise direction, starting from lower right-hand corner, through the 6.0 V emf source, then through the 4.0 Ω resistor before returning to the starting point in the lower right-hand corner (the loop rule can be applied to any round-trip loop in a circuit, even if there are other parts of this circuit):

"voltage supplied = voltage used,"

∆V_rises = ∆V_drops,

(6.0 V) = ΔV_resistor.

Then we can evaluate the "specialized" form for the power used by the resistor:

P_resistor = (ΔV_resistor)²/R_resistor,

P_resistor = (6.0 V)²/(4.0 Ω) = 9.0 W.

(This "specialized" equation for power should only be used if the voltage used by the circuit element is known already either from the loop rule (as was done here) or from Ohm's law.)

(Response (A) is the numerical value for the current flowing through the resistor; response (C) is ΔV_resistor·R_resistor; response (D) is ΔV_resistor)²·(R_resistor)².)

Sections 30882, 30883
Exam code: quiz05z0m6
(A) : 5 students
(B) : 19 students
(C) : 9 students
(D) : 1 student

Success level: 56%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.83