20.3 Resistance and resistivity  (Page 3/6)

 Page 3 / 6

The resistance of an object also depends on temperature, since ${R}_{0}$ is directly proportional to $\rho$ . For a cylinder we know $R=\mathrm{\rho L}/A$ , and so, if $L$ and $A$ do not change greatly with temperature, $R$ will have the same temperature dependence as $\rho$ . (Examination of the coefficients of linear expansion shows them to be about two orders of magnitude less than typical temperature coefficients of resistivity, and so the effect of temperature on $L$ and $A$ is about two orders of magnitude less than on $\rho$ .) Thus,

$R={R}_{0}\left(\text{1}+\alpha \Delta T\right)$

is the temperature dependence of the resistance of an object, where ${R}_{0}$ is the original resistance and $R$ is the resistance after a temperature change $\Delta T$ . Numerous thermometers are based on the effect of temperature on resistance. (See [link] .) One of the most common is the thermistor, a semiconductor crystal with a strong temperature dependence, the resistance of which is measured to obtain its temperature. The device is small, so that it quickly comes into thermal equilibrium with the part of a person it touches.

Calculating resistance: hot-filament resistance

Although caution must be used in applying $\rho ={\rho }_{0}\left(\text{1}+\alpha \Delta T\right)$ and $R={R}_{0}\left(\text{1}+\alpha \Delta T\right)$ for temperature changes greater than $\text{100º}\text{C}$ , for tungsten the equations work reasonably well for very large temperature changes. What, then, is the resistance of the tungsten filament in the previous example if its temperature is increased from room temperature ( $\text{20ºC}$ ) to a typical operating temperature of $\text{2850º}\text{C}$ ?

Strategy

This is a straightforward application of $R={R}_{0}\left(\text{1}+\alpha \Delta T\right)$ , since the original resistance of the filament was given to be ${R}_{0}=0\text{.}\text{350 Ω}$ , and the temperature change is $\Delta T=\text{2830º}\text{C}$ .

Solution

The hot resistance $R$ is obtained by entering known values into the above equation:

$\begin{array}{lll}R& =& {R}_{0}\left(1+\alpha \Delta T\right)\\ & =& \left(0\text{.}\text{350 Ω}\right)\left[\text{1}+\left(4.5×{\text{10}}^{–3}/\text{ºC}\right)\left(\text{2830º}\text{C}\right)\right]\\ & =& \text{4.8 Ω.}\end{array}$

Discussion

This value is consistent with the headlight resistance example in Ohm’s Law: Resistance and Simple Circuits .

Phet explorations: resistance in a wire

Learn about the physics of resistance in a wire. Change its resistivity, length, and area to see how they affect the wire's resistance. The sizes of the symbols in the equation change along with the diagram of a wire.

Section summary

• The resistance $R$ of a cylinder of length $L$ and cross-sectional area $A$ is $R=\frac{\mathrm{\rho L}}{A}$ , where $\rho$ is the resistivity of the material.
• Values of $\rho$ in [link] show that materials fall into three groups— conductors, semiconductors, and insulators .
• Temperature affects resistivity; for relatively small temperature changes $\Delta T$ , resistivity is $\rho ={\rho }_{0}\left(\text{1}+\alpha \Delta T\right)$ , where ${\rho }_{0}$ is the original resistivity and $\text{α}$ is the temperature coefficient of resistivity.
• [link] gives values for $\alpha$ , the temperature coefficient of resistivity.
• The resistance $R$ of an object also varies with temperature: $R={R}_{0}\left(\text{1}+\alpha \Delta T\right)$ , where ${R}_{0}$ is the original resistance, and $R$ is the resistance after the temperature change.

Conceptual questions

In which of the three semiconducting materials listed in [link] do impurities supply free charges? (Hint: Examine the range of resistivity for each and determine whether the pure semiconductor has the higher or lower conductivity.)

Questions & Answers

find the density of a fluid in which a hydrometer having a density of 0.750g/mL floats with 92.0% of its volume submerged.
Neshrin Reply
Uniform speed
Sunday
(a)calculate the buoyant force on a 2.00-L Helium balloon.(b) given the mass of the rubber in the balloon is 1.50g. what is the vertical force on the balloon if it is let go? you can neglect the volume of the rubber.
Neshrin Reply
To Long
Usman
pleaseee. can you get the answer? I can wait till 12
Neshrin
a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
Bala Reply
how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
Bala
what is the difference between atomic physics and momentum
Nana Reply
find the dimensional equation of work,power,and moment of a force show work?
Emmanuel Reply
What's sup guys
Peter
cul and you all
Okeh
cool you bro
Nana
so what is going on here
Nana
hello peeps
Joseph
Michelson Morley experiment
Riya Reply
how are you
Naveed
am good
Celine
you
Celine
hi
Bala
Hi
Ahmed
Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
the answer is 9.2m/s
OBERT
express your height in Cm
Emmanuel Reply
my project is Sol gel process how to prepare this process pls tell me
Bala
the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
Emmanuel Reply
KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
Manyo
thanks jare
Doc
Thanks
AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
AMADI
what is physic
zalmia Reply
please gave me answar
zalmia
Study of matter and energy
Fagbenro
physics is the science of matter and energy and their interactions
Acquah
physics is the technology behind air and matter
Doc
Okay
William
hi sir
Bala
how easy to understanding physics sir
Bala
Easy to learn
William

Read also:

Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

 By By By By Danielrosenberger