Anyone know derivation of ohm's law formula V=I x R.?

Question

Start from definition of resistivity,charge of electron,cross sectional area,...etc. I have seen this in a electrical engineering book but cannot recall.Ohm's formula is very fanous and simple.But how he got this formula is not so simple.

Answer 1

There is no "derivation" of Ohm's Law. It is based entirely on the results of experiment. In fact, not all conductors obey Ohm's Law... they're called non-Ohmic conductors.

Further, even conductors that DO obey Ohm's Law do not obey it for all values of applied potential difference, V.

Answer 2

Derivation Of Ohms Law

Answer 3

Hmmm some of the reasoning looks a little circular.
I have done this with Boyles law. That is assuming that electrons are like molecules in a gas. Heat therefore plays a big part, as it should. I will look into this and get back to you. Or maybe some genius will take up what i am saying.

Where I am coming from is that resistivity seems to be derived from resistance which is derived from Ohm's law.
A true derivation establishes a proportional relationship between current and voltage. Then Ohm's law can be found; things to consider are length of route, crossectional area, temperature. Conductors that increase their resistance in direct proportion to temperature are called 'Ohmic' conductors. A quick way to derive might be to find cosider power of a resistor being the heat it emits and comparing it to the VXI and I^2X 'something'
The something being resistance (I^2 R)

Answer 4

The derivation of V=IR starts with the assumption that
J=sigma*f
J= current density
sigma = conductivity
f = force per unit charge
now f is simply the Lorenz for E + v x B
so
J=sigma (E + v x B) this is ohms law
now in most cases v x B is assumed to be zero
this leaves
J = sigma * E
J= I/A (current / area)
sigma = 1/rho (1/resistivity)
so R = L/(sigma * A)
or
sigma = L/RA
going back to ohms law

I/A=L/RA* E
I*R= L * E
L*E =V
IR=V

This is a poor proof and should really be done with integrals but that would be hard to type here but this should give you enough info to do that proof on your own. Also ohms laws only holds in certain cases. It breaks down when space charge limits the current. Then you need to use the Child-Langmuir law.

Answer 5

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A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohm's law: V = IROhm's law states that, in an electrical circuit, the current passing through most materials is directly proportional to the potential difference applied across them.

In mathematical terms, this is written as:

,
where I is the current, V is the potential difference, and R is a proportionality constant called the resistance. The potential difference is also known as the voltage drop, and is sometimes designated by E or U instead of V.

The SI unit of current is the ampere; that of potential difference is the volt; and that of resistance is the ohm, equal to one volt per ampere. The law is named after the physicist Georg Ohm, who published it in 1826.

Answer 6

Resistance, is the natural property of an object to resist electrical current. So the higher the resistance the tougher it is to 'drive' a current through the object. But if we multiply that by the amount of current going through, we are given the 'potential drop' or voltage that it requires to drive the current through the object

Volts=Joules/Coulomb I=Coulomb/sec R=Joules times seconds/coulombs^2