# F = ma & Ohm law CONFLICT

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#### Rushi Shroff

http://www.maztravel.com/maz/explain/ohm.html

current density (I) = The number of atoms per unit volume (N) times
the number of free electrons per atom (f) times
the charge per electron (q) times
the average velocity of the electron (1/2 A * T)
thus: I = 1/2 * N * f * q * A * T

now acceleration A = Force / mass of electron (m) = E / m
and time T = distance between collision L / thermal Velocity V
so I = (N * f * L * q^2 / 2 m V) * E
What have we here? Well, we can see that the stuff in the parentheses, which are all things that depend on the material the wire is made of, is a first order formula for the conductivity. Conductivity is the inverse of resistance, so if we stick all that stuff on the other side of the equation we get:

V (voltage) = (2 m V / N * f * L * q^2) I .... Ohm's law
Which correctly predicts that the resistance should increase as the thermal velocity of the electrons gets larger, or in other words, resistance goes up with temperature, a well know fact.

Now the resistance of a metal like copper is essentially zero, but the resistance of the bulb is substantial. Thus there are a lot more collisions taking place in the filament than in the wire, and guess what, the filament gets hot. The electrical force is being converted into heat, and eventually light by the resistance of the filament, in other words, the flashlight produces light.