Download From last time Resistivity Example Problem

2/3/11
From last time
Announcements
• My office hours are today from 2 – 3 pm
•  or by appointment
• WebAssign HW Set 4 due this Friday
•  Problems cover material from Chapters 17
• Exam 1 8:20 – 10:10 pm Wednesday, February 16
•  Covers Ch. 15-18
•  20 questions
•  Room assignments:
Drift speed:
n 
Resistivity
ΔQ
Δt
ΔV = I R
R= ρ
lL
A
Example Problem
The resistance of an ohmic conductor is
proportional to its length, L, and
inversely proportional to its crosssectional area, A
n 
n 
Resistance/
Ohm’s Law
Resistivity
R= ρ
Current: Iav ≡
n 
QUESTIONS? PLEASE ASK!
n 
n 
lL
A
ρ is the constant of proportionality and is
called the resistivity of the material
n 
17.12 Suppose you wish to
fabricate a uniform wire out of 1 g
of copper. If the wire is to have a
resistance R = 0.50 Ω, and if all of
the copper wire is to be used, what
will be the (a) length and (b)
diameter of the wire?
1
2/3/11
Temperature Variation of
Resistivity/Resistance
n 
Example Problem
For most metals, resistivity increases
approximately linearly with temperature over a
limited temperature range
n 
ρ = ρo [1 + α(T − To )]
n 
n 
n 
ρ=resistivity at T; ρo=resistivity at To(typically 20° C)
α is the temperature coefficient of resistivity
… and resistance is proportional to the
resistivity, so…
R = Ro [1 + α(T − To )]
Electrical Energy in a
Circuit
n 
Energy ΔQΔV provided by the
battery (AàB) is lost in the
resistor(CàD)
n 
n 
n 
Recall PE = qΔV
The rate at which the energy
is lost is
ΔQ
℘=
ΔV = I ΔV
Δt
Two other ways to write this:
℘ = I 2R =
ΔV 2
R
17.30 A toaster rated
at 1050 W operates on
a 120 V household
circuit and uses a 4.00
m length of Nichrome
wire as its heating
element. The
operating temperature
of this element is
320°C. What is the
cross-sectional area of
the wire?
Example Problem
n 
17.40 A certain toaster has a
heating element made of
Nichrome resistance wire. When
the toaster (at 20°C) is first
connected to 120 V source, the
initial current is 1.80 A, but the
current decreases when the
element heats up. When the
toaster reaches it final
temperature, the current is 1.53
A. (a) Find the power the toaster
produces at its final
temperature. (b) What is the
final temperature?
2
2/3/11
Superconductors
n 
n 
n 
Solution to 17.12
Remarkable materials!
R à 0 below a critical
temperature, TC
above TC, behave as
normal metals, but
suddenly drops to zero at
TC
Solution to 17.30
Solution to 17.40
3