Resistance from Microscopic Ohm's law

In summary, the task is to calculate the resistance of a simple cylindrical resistor made of a material with conductivity \sigma, length L, and cross-sectional area A. Using Ohm's Law, the resistance can be expressed as R = L/\sigmaA, where J = \sigmaE is the current density.
  • #1
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Homework Statement



Your task is to calculate the resistance of a simple cylindrical resistor with wires connected to the ends, such as the carbon composition resistors that are used on electronic circuit boards. Imagine that the resistor is made by squirting material whose conductivity is [tex]\sigma[/tex] into a cylindrical mold with length L and cross-sectional area A. Assume that this material satisfies Ohm's law. (It should if the resistor is operated within its power dissipation limits.)

What is the resistance R of this resistor?
Express the resistance in terms of variables given in the introduction. Do not use V or I in your answer.

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Homework Equations



J=[tex]\Sigma[/tex]E
V=EL
I=JA
R = V/I

The Attempt at a Solution



I start out with Ohm's Law and get resistence R to be R = V/I and I know V = EL and I = JA so I get resistence R to be R = EL/JA. I also know J = [tex]\Sigma[/tex]E. So I get resistence R to be R = EL/[tex]\Sigma[/tex]EA

Would the two E's cancel out?
 
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  • #2
I will continue from your R = EL/JA expression.
J = [tex]\sigma[/tex]E
therefore,
R = EL/[tex]\sigma[/tex]EA
the E's cancel out and your answer should be R = L/[tex]\sigma[/tex]A

Hope this helps.
 
  • #3
Ah, wrong sigma. Got it, thanks.
 

Related to Resistance from Microscopic Ohm's law

1. What is Microscopic Ohm's law?

Microscopic Ohm's law is a fundamental law in physics that describes the relationship between electric current, voltage, and resistance in a conductor. It states that the current through a conductor is directly proportional to the voltage applied, and inversely proportional to the resistance of the conductor.

2. How does resistance affect electric current?

Resistance is a measure of how much a material opposes the flow of electric current. According to Microscopic Ohm's law, as resistance increases, the current decreases. This means that a higher resistance in a conductor will result in a lower flow of current.

3. What factors affect resistance?

The resistance of a material depends on several factors, including the material's length, cross-sectional area, and temperature. Longer and thinner materials tend to have higher resistance, while shorter and thicker materials have lower resistance. Additionally, as the temperature of a material increases, its resistance also increases.

4. How can resistance be measured?

Resistance can be measured using a tool called a multimeter. This device can measure the voltage and current in a circuit and calculate the resistance using Ohm's law. Additionally, resistance can also be calculated by measuring the length, cross-sectional area, and temperature of a material and using the appropriate formulas.

5. What are some real-world applications of Microscopic Ohm's law?

Microscopic Ohm's law has many practical applications, including the design of electrical circuits and devices, such as resistors, capacitors, and transistors. It is also used in industries such as electronics, telecommunications, and power generation to understand and control the flow of electricity. Additionally, it is a crucial concept in fields such as electrical engineering, physics, and chemistry.

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