# 9.3 Resistivity and resistance  (Page 6/10)

 Page 6 / 10

Check Your Understanding The resistance between the two conductors of a coaxial cable depends on the resistivity of the material separating the two conductors, the length of the cable and the inner and outer radius of the two conductor. If you are designing a coaxial cable, how does the resistance between the two conductors depend on these variables?

The longer the length, the smaller the resistance. The greater the resistivity, the higher the resistance. The larger the difference between the outer radius and the inner radius, that is, the greater the ratio between the two, the greater the resistance. If you are attempting to maximize the resistance, the choice of the values for these variables will depend on the application. For example, if the cable must be flexible, the choice of materials may be limited.

View this simulation to see how the voltage applied and the resistance of the material the current flows through affects the current through the material. You can visualize the collisions of the electrons and the atoms of the material effect the temperature of the material.

## Summary

• Resistance has units of ohms $\left(\text{Ω}\right)$ , related to volts and amperes by $1\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}1\phantom{\rule{0.2em}{0ex}}\text{V/A}$ .
• The resistance R of a cylinder of length L and cross-sectional area A is $R=\frac{\rho L}{A}$ , 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 $\text{Δ}T$ , resistivity is $\rho ={\rho }_{0}\left(1+\alpha \text{Δ}T\right)$ , where ${\rho }_{0}$ is the original resistivity and $\alpha$ is the temperature coefficient of resistivity.
• The resistance R of an object also varies with temperature: $R={R}_{0}\left(1+\alpha \text{Δ}T\right)$ , where ${R}_{0}$ is the original resistance, and R is the resistance after the temperature change.

## Conceptual questions

The IR drop across a resistor means that there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor? Explain.

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

In carbon, resistivity increases with the amount of impurities, meaning fewer free charges. In silicon and germanium, impurities decrease resistivity, meaning more free electrons.

Does the resistance of an object depend on the path current takes through it? Consider, for example, a rectangular bar—is its resistance the same along its length as across its width?

If aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?

Copper has a lower resistivity than aluminum, so if length is the same, copper must have the smaller diameter.

## Problems

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is $3.60\phantom{\rule{0.2em}{0ex}}\text{Ω}$ ?

Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows.

$R=6.750\phantom{\rule{0.2em}{0ex}}\text{k}\phantom{\rule{0.2em}{0ex}}\text{Ω}$

How many volts are supplied to operate an indicator light on a DVD player that has a resistance of $140\phantom{\rule{0.2em}{0ex}}\text{Ω}$ , given that 25.0 mA passes through it?

What is the resistance of a 20.0-m-long piece of 12-gauge copper wire having a 2.053-mm diameter?

$R=0.10\phantom{\rule{0.2em}{0ex}}\text{Ω}$

The diameter of 0-gauge copper wire is 8.252 mm. Find the resistance of a 1.00-km length of such wire used for power transmission.

If the 0.100-mm-diameter tungsten filament in a light bulb is to have a resistance of $0.200\phantom{\rule{0.2em}{0ex}}\text{Ω}$ at $20.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , how long should it be?

$\begin{array}{c}R=\rho \frac{L}{A}\hfill \\ L=3\phantom{\rule{0.2em}{0ex}}\text{mm}\hfill \end{array}$

A lead rod has a length of 30.00 cm and a resistance of $5.00\phantom{\rule{0.2em}{0ex}}\mu \text{Ω}$ . What is the radius of the rod?

Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance per unit length (as they might in household wiring).

$\frac{{R}_{\text{Al}}}{{L}_{\text{Al}}}}{{R}_{\text{Cu}}}{{L}_{\text{Cu}}}}=\frac{{\rho }_{\text{Al}}\frac{1}{\pi {\left(\frac{{D}_{\text{Al}}}{2}\right)}^{2}}}{{\rho }_{\text{Cu}}\frac{1}{\pi {\left(\frac{{D}_{\text{Cu}}}{2}\right)}^{2}}}=\frac{{\rho }_{\text{Al}}}{{\rho }_{\text{Cu}}}{\left(\frac{{D}_{\text{Cu}}}{{D}_{\text{Al}}}\right)}^{2}=1,\phantom{\rule{0.8em}{0ex}}\frac{{D}_{\text{Al}}}{{D}_{\text{Cu}}}=\sqrt{\frac{{\rho }_{\text{Al}}}{{\rho }_{Cu}}}$

What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when $1.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{V}$ is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)

(a) To what temperature must you raise a copper wire, originally at $20.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , to double its resistance, neglecting any changes in dimensions? (b) Does this happen in household wiring under ordinary circumstances?

a. $R={R}_{0}\left(1+\alpha \text{Δ}T\right),\phantom{\rule{0.8em}{0ex}}2=1+\alpha \text{Δ}T,\phantom{\rule{0.8em}{0ex}}\text{Δ}T=256.4\phantom{\rule{0.2em}{0ex}}\text{°C},\phantom{\rule{0.8em}{0ex}}T=276.4\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ ;
b. Under normal conditions, no it should not occur.

A resistor made of nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at $20.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ . Over what temperature range can it be used?

Of what material is a resistor made if its resistance is 40.0% greater at $100.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ than at $20.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ ?

$\begin{array}{ccc}\hfill R& =\hfill & {R}_{0}\left(1+\alpha \text{Δ}T\right)\hfill \\ \hfill \alpha & =0.006\phantom{\rule{0.2em}{0ex}}\text{°}{\text{C}}^{-1}\hfill \end{array}$ , iron

An electronic device designed to operate at any temperature in the range from $-10.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ to $55.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ contains pure carbon resistors. By what factor does their resistance increase over this range?

(a) Of what material is a wire made, if it is 25.0 m long with a diameter of 0.100 mm and has a resistance of $77.7\phantom{\rule{0.2em}{0ex}}\text{Ω}$ at $20.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ ? (b) What is its resistance at $150.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C?}$

a. $R=\rho \frac{L}{A},\phantom{\rule{0.8em}{0ex}}\rho =2.44\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-8}\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}·\text{m}$ , gold;
b. $\begin{array}{c}R=\rho \frac{L}{A}\left(1+\alpha \text{Δ}T\right)\hfill \\ \\ \\ \\ R=2.44\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-8}\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}·\text{m}\left(\frac{25\phantom{\rule{0.2em}{0ex}}\text{m}}{\pi {\left(\frac{0.100\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\text{m}}{2}\right)}^{2}}\right)\left(1+0.0034\phantom{\rule{0.2em}{0ex}}\text{°}{\text{C}}^{-1}\left(150\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}-20\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\right)\right)\hfill \\ R=112\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}\hfill \end{array}$

Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at $20.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ ?

A copper wire has a resistance of $0.500\phantom{\rule{0.2em}{0ex}}\text{Ω}$ at $20.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C},$ and an iron wire has a resistance of $0.525\phantom{\rule{0.2em}{0ex}}\text{Ω}$ at the same temperature. At what temperature are their resistances equal?

$\begin{array}{c}{R}_{\text{Fe}}=0.525\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.8em}{0ex}}{R}_{\text{Cu}}=0.500\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.8em}{0ex}}{\alpha }_{\text{Fe}}=0.0065\phantom{\rule{0.2em}{0ex}}\text{°}{\text{C}}^{-1}\phantom{\rule{0.8em}{0ex}}{\alpha }_{\text{Cu}}=0.0039\phantom{\rule{0.2em}{0ex}}\text{°}{\text{C}}^{-1}\hfill \\ {R}_{\text{Fe}}={R}_{\text{Cu}}\hfill \\ {R}_{0\phantom{\rule{0.2em}{0ex}}\text{Fe}}\left(1+{\alpha }_{\text{Fe}}\left(T-{T}_{0}\right)\right)={R}_{0\phantom{\rule{0.2em}{0ex}}\text{Cu}}\left(1+{\alpha }_{\text{Cu}}\left(T-{T}_{0}\right)\right)\hfill \\ \frac{{R}_{0\phantom{\rule{0.2em}{0ex}}\text{Fe}}}{{R}_{0\phantom{\rule{0.2em}{0ex}}\text{Cu}}}\left(1+{\alpha }_{\text{Fe}}\left(T-{T}_{0}\right)\right)=1+{\alpha }_{\text{Cu}}\left(T-{T}_{0}\right)\hfill \\ T=2.91\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\hfill \end{array}$

what is flux
Total number of field lines crossing the surface area
Kamru
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
prince
what is temperature change
Celine
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
Celine
process whereby the degree of hotness of a body (or medium) changes
Salim
Q=mcΔT
Salim
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
Salim
what was the temperature of the soft drink when it was removed ?
Salim
15 degree Celsius
Celine
15 degree
Celine
ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
Salim
0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
Salim
what is d final ans for Fahrenheit and Celsius
Celine
it said what is temperature change in Fahrenheit and Celsius
Celine
the 15 is already in Celsius
Salim
So the final answer for Fahrenheit is 59
Salim
what is d final ans for Fahrenheit and Celsius
Celine
what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
Jorge
besides increasing the capacitance, is there any?
Bundi
mechanical stiffness and small size
Jorge
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
what is flux
Bundi
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
PATRICK
somebody help me answer the question above
PATRICK
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
what are the elementary compositions of a cell?
poles, chemical
prabir
when a current pass through a material does the velocity varies
no.
prabir
what is spin entropy ?and disorder in ferromagnetic material
diagram of an hall effect sensor
if a magnetised wire having dipole moment M is bent in the form of arc subtending angle of 45°at centre,new magnetic moment is
prabir
is this book for preparing IIT or neet?
is it possible to increase the temperature of a gas without adding heat to it?
I'm not sure about it, but I think it's possible. If you add some form of energy to the system, it's a possibility. Also, if you change the pression or the volume of the system, you'll increase the kinetic energy of the system, increasing the gas temperature. I don't know if I'm correct.
playdoh
For example, if you get a syringe and close the tip(sealing the air inside), and start pumping the plunger, you'll notice that it starts getting hot. Again, I'm not sure if I am correct.
playdoh
you are right for example an adiabatic process changes all variables without external energy to yield a temperature change. (Search Otto cycle)
when a current pass through a material does the velocity varies
lovet
yes at adiabatic compression temperature increase
Nepal
how to draw a diagram of a triode
whate is fckg diagrame?
Arzoodan
why do we use integration?
To know surfaces below graphs.
Jan
To find a Primitive function. Primitive function: a function that is the origin of another
playdoh
yes
Dharmdev
what is laps rate
Dharmdev
Г=-dT/dZ that is simply defination
Arzoodan
what is z
Dharmdev
to find the area under a graph or to accumulate .e.g. sum of momentum over time is no etic energy.
Naod
Z is alt.,dZ altv difference
Arzoodan