Resistivity and Ohm's Law question

In summary, a long wire connected to a 12V battery with 6.4 x 10^19 electrons passing through a cross section each second has a resistance of 1.2Ω. The resistance was calculated using the equation R=V/I, where the charge (q) was found using the number of electrons (n) and the current (I) was determined by dividing the charge by the time (T). The mistake in the original calculation was using the electron mass instead of the electron charge.
  • #1
Vickyvicksss
5
0

Homework Statement


A long wire connected to the terminals of a 12V battery has 6.4 x 1019 electrons passing a cross section of wire each second. calculate it's resistance.

answer is 1.2Ω

Homework Equations


q = ne
q = IE
R=ρ L/A

The Attempt at a Solution


V= 12v
n= 6.4 x 1019 electrons
R=?

First I used the number of electrons to find my charge (q)
q = ne
q = (6.4 x 1019) ( 9 x 10-31)
q = 5.76 x 10 -11

Then calculating my current
I= Q/T
Im assuming T is 1s, because it says "passing a cross section of wire each second"
I = 5.76 x 10 -11/ 1
I= 5.76 x 10 -11

Then i calculated my resistance
R= V/R
R= 12/5.76 x 10 -11
R= 2.0 x 1011

What am i doing wrong? D:
 
Physics news on Phys.org
  • #2
The charge of an electron is e=1.6(10-19) C.
 
  • #3
q = ne
q = (6.4 x 1019) ( 9 x 10-31)
... that would be the electron mass.

e=1.60217646×10-19 Coulombs
 
  • #4
rock.freak667 said:
The charge of an electron is e=1.6(10-19) C.

Simon Bridge said:
... that would be the electron mass.

e=1.60217646×10-19 Coulombs

LOL! CRAP! i knew that~ :) Thank you :3 I was going insane for a bit.
 
  • #5
Happens to the best of us :-)
 

1. What is resistivity and how is it different from resistance?

Resistivity is a measure of a material's ability to resist the flow of electricity. It is a characteristic of the material and is measured in ohm-meters (Ωm). Resistance, on the other hand, is a measure of how much a material impedes the flow of electricity and is dependent on the length, cross-sectional area, and resistivity of the material.

2. What is Ohm's Law and how is it related to resistivity?

Ohm's Law states that the current through a conductor is directly proportional to the voltage across it, given a constant temperature. This relationship can be expressed mathematically as V = IR, where V is voltage, I is current, and R is resistance. This means that resistivity, which is a measure of a material's resistance, is directly related to the amount of current that can flow through it for a given voltage.

3. How does temperature affect resistivity?

The resistivity of most materials increases with an increase in temperature. This is because as the temperature increases, the atoms in the material vibrate more, causing more collisions with the electrons and increasing the resistance to current flow. However, there are some materials, such as semiconductors, that show a decrease in resistivity with an increase in temperature.

4. What is the difference between conductors, insulators, and semiconductors?

Conductors are materials that allow electricity to flow easily through them due to their low resistivity. Insulators, on the other hand, have high resistivity and do not allow electricity to flow through them easily. Semiconductors have a resistivity that falls between that of conductors and insulators and their conductivity can be controlled by adding impurities or applying an electric field.

5. How is resistivity measured in a material?

Resistivity can be measured using a device called an ohmmeter, which applies a known voltage to the material and measures the resulting current. The resistivity can then be calculated using Ohm's Law (R = V/I) and the dimensions of the material. Alternatively, the resistivity can be determined by measuring the resistance of a sample with known dimensions and using the formula ρ = RA/L, where ρ is resistivity, R is resistance, A is cross-sectional area, and L is length.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
551
  • Introductory Physics Homework Help
Replies
2
Views
735
  • Introductory Physics Homework Help
Replies
18
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
369
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
803
  • Introductory Physics Homework Help
Replies
21
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top