Physics quiz question: USB-C communication connection wire power dissipation

Physics 205B Quiz 5, spring semester 2017
Cuesta College, San Luis Obispo, CA

The communication connection wire within a Type-C USB cable has a resistance of 5.6 kΩ, and while attached to a smartphone, 80 µA of current passes through this wire. While this current passes through the communication connection wire, the electrical power dissipated within it is:
(A) 1.4⨉10^–8 W.
(B) 3.6⨉10^–5 W.
(C) 0.45 W.
(D) 2.5⨉10³ W.

[*] androidauthority.com/usb-type-c-and-3-1-explained-656552/.

Correct answer (highlight to unhide): (B)

Given the resistance R and the current I that passes through the communication connection wire, the voltage drop across it is given by Ohm's law:

∆V = I·R,

∆V = (80⨉10^–6 A)·(5.6⨉10³ Ω) = 0.448 V.

The power dissipated in the communication connection wire is then:

P = I·∆V,

P = (80⨉10^–6 A)·(0.448 V) = 0.00003584 W,

or to two significant digits, 3.6⨉10^–5 W.

Alternatively, the power can be directly calculated by making a substitution for ∆V using Ohm's law:

P = I·∆V = I·(I·R),

P = I²·R,

P = (80⨉10^–6 A)²·((5.6⨉10³ Ω) = 3.6⨉10^–5 W.

(Response (A) is I/R; response (C) is ∆V = I·R; and response (D) is ∆V·R= I·R².)

Sections 30882, 30883
Exam code: quiz05vLeY
(A) : 6 students
(B) : 17 students
(C) : 0 students
(D) : 3 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.86