Explaining I^2R=J_c/σ Relationship

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In summary, I^2R=J_c/σ is a mathematical relationship that describes the flow of electric current through a material with a certain resistance. It is important for understanding and calculating the behavior of electric current and heat generation in different materials. This relationship is derived from Ohm's Law and the definition of current density. The material's resistance and electrical conductivity, as well as temperature, can affect this relationship. In practical applications, it is used to calculate power dissipation and temperature rise in electronic components, as well as in designing and optimizing electrical systems.
  • #1
lavster
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can someone explain how these two are equal:

[tex]I^2 R = J_c \cdot \frac{J_c}{\sigma}[/tex]

where I is the current, R is resistance, J_c is conduction current density, and [tex]\sigma[/tex] is the conductivity.

thanks
 
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  • #2
They don't seem to be equal so there is nothing to explain.
You can just look at the units. The right hand side is power density (W/m^3) and the left hand side is just power (Watt)
 
  • #3
I=[A]
R=[Ohm]
J=[A/m^2]
sigma=[1/(Ohm*m)]

you have a problem there with units :)
 

FAQ: Explaining I^2R=J_c/σ Relationship

What is the meaning of I^2R=J_c/σ?

I^2R=J_c/σ is a mathematical relationship that describes the flow of electric current (I) through a material with a certain resistance (R). It states that the amount of heat generated (I^2R) is equal to the amount of current density (J_c) divided by the electrical conductivity (σ).

Why is it important to understand the I^2R=J_c/σ relationship?

This relationship is important because it helps us understand the behavior of electric current in different materials. It also allows us to calculate the amount of heat generated and the resulting temperature changes in a material.

How is the I^2R=J_c/σ relationship derived?

The I^2R=J_c/σ relationship is derived from Ohm's Law (V=IR) and the definition of current density (J_c=I/A), where V is voltage, I is current, R is resistance, and A is cross-sectional area. By substituting J_c=I/A into Ohm's Law and solving for I^2R, we get the final relationship.

What factors affect the I^2R=J_c/σ relationship?

The I^2R=J_c/σ relationship is affected by the material's resistance (R) and electrical conductivity (σ). Temperature can also have an impact, as it can alter the material's resistance and conductivity.

How is the I^2R=J_c/σ relationship used in practical applications?

In practical applications, the I^2R=J_c/σ relationship is used to calculate the power dissipation and temperature rise in electronic components, such as resistors and wires. It is also helpful in designing and optimizing electrical systems to ensure efficient use of energy and avoid overheating.

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