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Gigacore
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I'm still a intermediate science student. I'm not understanding how to derive the ohm's law. can anyone help me?
ZapperZ said:It isn't derived in intro physics,
ZapperZ said:Actually, you CAN derive Ohm's law. It isn't derived in intro physics, but I think most people who take Solid State Physics see this in almost the first week of class when dealing with the http://people.seas.harvard.edu/~jones/es154/lectures/lecture_2/drude_model/drude_model.html.
When you arrive at [itex]J = \sigma E[/itex], that is essentially Ohm's Law if you remember that J is current crossing an area A, [itex]\sigma[/itex] is [itex]1/\rho[/itex] where [itex]\rho[/itex] is the resistivity, and E is change in potential over a unit length. So you do end up with Ohm's Law.
Zz.
Then what do you call the thing in Zz's link?dhris said:It depends on what you call "Ohm's Law". I believe it is common to call [tex]{\bf J}=\sigma {\bf E}[/tex] Ohm's law, and V=IR is a special case of it. In this view, there is indeed no derivation
dhris said:It depends on what you call "Ohm's Law". I believe it is common to call [tex]{\bf J}=\sigma {\bf E}[/tex] Ohm's law, and V=IR is a special case of it. In this view, there is indeed no derivation as it is essentially observational (although I believe you can use statistical mechanics to justify it in some way).
Gigacore said:I'm still a intermediate science student. I'm not understanding how to derive the ohm's law. can anyone help me?
ZapperZ said:Er.. that's puzzling. The whole thing was derived using the statistical distribution of free electrons, which is the starting point of the Drude model. So how is it not a derivation?
And I've only shown the simplest case. I could have easily pointed to the Boltzmann transport equation where a more rigorous derivation can be shown in which the Drude model is a special case.
Zz.
dhris said:Sorry! I misunderstood your answer (and didn't notice your link). I assumed that by "derivation" Gigacore was asking how Ohm's Law follows from the laws of electrodynamics, i.e. Maxwell's equations, and nothing more complicated than that.
Anyway, as a kind of related comment on the statistical mechanical models, I always had the feeling that the agreement with the empirically-established Ohm's Law was taken as a justification of the original assumptions, and not that I was seeing a convincing derivation. Even with the Boltzmann equation I seem to recall that you need some simplifying assumptions to get anything useful, which are then justified by the result. It was awhile ago that I encountered these things, so please correct me if this feeling is way off.
Manchot said:Well, the easiest way to "derive" it is to Taylor-expand the voltage across the resistor in terms of the current around a voltage of zero, drop the quadratic and higher order terms, and note that the current should be zero when the voltage is zero. Then, identify the resistance as dV/dI, and you're set. (Obviously, this doesn't give you much physics.)
ZapperZ said:Er.. you can't derive Ohm's Law from maxwell equations because of one important thing - you need to know how to treat a bunch of charges moving at random, which isn't contained in Maxwell equation. That's why statistical physics comes in here.
ZapperZ said:Actually, you CAN derive Ohm's law. It isn't derived in intro physics, but I think most people who take Solid State Physics see this in almost the first week of class when dealing with the http://people.seas.harvard.edu/~jones/es154/lectures/lecture_2/drude_model/drude_model.html.
When you arrive at [itex]J = \sigma E[/itex], that is essentially Ohm's Law if you remember that J is current crossing an area A, [itex]\sigma[/itex] is [itex]1/\rho[/itex] where [itex]\rho[/itex] is the resistivity, and E is change in potential over a unit length. So you do end up with Ohm's Law.
Zz.
Ohm's Law is a fundamental law in physics that explains the relationship between voltage, current, and resistance in an electrical circuit. It states that the current flowing through a conductor is directly proportional to the voltage and inversely proportional to the resistance.
To derive Ohm's Law, you need to start with the equation for electric power, P = VI, where P is power in watts, V is voltage in volts, and I is current in amps. Then, you can use the definition of resistance, R = V/I, to substitute for V in the power equation. This will give you the final equation of P = I2R.
Ohm's Law is significant because it helps us understand the behavior of electricity in a circuit. It allows us to calculate the amount of current flowing through a conductor, the voltage drop across a component, and the resistance of a material. This knowledge is essential in designing and troubleshooting electrical circuits and systems.
Ohm's Law has a wide range of real-life applications, including household electrical systems, electronic devices, and automotive systems. For example, it can help you calculate the correct size of wire to use for a particular circuit, determine the appropriate resistor to use in an LED circuit, or troubleshoot a malfunctioning electronic device.
Ohm's Law is applicable to most electrical circuits, as long as the temperature and other environmental factors remain constant. However, there are some exceptions, such as circuits containing non-ohmic materials like diodes and transistors, where Ohm's Law does not hold true. In these cases, more advanced laws and equations must be used to analyze the circuit.