OHM

CURRENT

Imagining the free electrons of the band of conduction of a conductor like an electron gas (Drude's model), these move fastly inside the conductor.
We can't perceive this movement because the electrons move in every directions but, thinking to cross the conductor with an imaginary plan, we can observe a flow of loads ( electrical current) that it corresponds to

Creating a potential difference inside the solid we created and electric field

he electrons are accelerated by a force

and according to the second principle of dynamics the acceleration is

In the model of perfect gases, here applied to electrons, the volumes are consider null and so they moves in an empty place; but the electrons are in an atmosphere where the other same elestrons are present, therefore they are taken place hits between atoms, where nucleus absorb the cinetic energy of the electrons, energy that will come converted in thermal (called Joule's effect). The drift speed that one that allows the passage of current from a smaller to a bigger potential

Applying the model of dynamics of the fluid we obtains

the loads results as

The density of loads that it will be directed in the same direction of the current is

the product of constants at the second member is calle RESISTANCE

measured in Ω.
This expression represents the first law of Ohm

the current that slides through conductor is always directly proporzional to the potential difference applied to the same instrument

it can be indicated resistivity

this is the second Ohm's law

in the conductors the resistance it depends on the geometric configuration of the conductor and from the material of which it is constituted

CIRCUIT

In order to verify the Ohm's laws it is necessary to compose a circuit composed by

an alternator that produce 4.5V ;
reostato an instrument to obtain a variable voltage, is composed by a conductor and a spiraliform winding that uses the second Ohm's law (the resistance is is proporzional them to the length of the conductor); with a mobile cursor, composed by an insulating material, is possible to change the contacts.
amperometer, the misures the current;
a voltmeter, that indicate the voltage, connected in parallel to the circuit;
a resistence

The connections between the several members of the circuits, whose resistence is considered null

ESPERIMENT

Analyzing vary cases, we consider thesensibility of the scale of amperometer as 0,05 A and that one of the voltmetro as 0,02V

COSTANTANA (40%Ni-60%Cr)

V (Volt)	4.0	3.5	3.0	2.5	2.0	1.5	1.0	0.5
i (Ampere)	1.6	1.4	1.2	1.0	0.8	0.6	0.4	0.2

R=2.5 Ω

Ni-Cr 0.56mm

V (Volt)	5.1	4.0	3.0	2.5	2.0	1.0
i (Ampere)	1.6	1.3	1.1	0.8	0.6	0.3

R=(3.2±0.1)

Ni-Cr0.70mm

V (Volt)	5.0	4.0	3.0	2.0	1.0
i (Ampere)	1.7	1.35	1.0	0.7	0.35

R=(2.8±0.2)

Ni-Cr

V (Volt)	5.1	4.0	3.0	2.0
i (Ampere)	0.85	0.65	0.4	0.25

R=(7±1)

Ni-Cr 0.70 in series

V (Volt)	5.1	4.0	3.0	2.0	1.0
i (Ampere)	0.85	0.65	0.5	0.35	0.15

R=(6.1±0.3)

Ni-Cr 0.70 in parallel

V (Volt)	1.30	1.00	0.75	0.50	0.25
i (Ampere)	0.95	0.75	0.55	0.4	0.2

R=(1.4±0.1)

CONCLUSIONS

Remember various factors that affect the values :

in the reading of the measures we can commit parallax error;
the conductors are crossing by much currents so their thenght are varied
because thermal energy that involves a greater number of hits between atoms, so the values of the resistence are a few bigger then the real values.
the alternation produced a not stable voltage
the nodes are the points of greater dispersion, and seen the structure of the circuit can be asserted that being high the number of the connections this spread is remarkable;
as already said previously the resistances of the connections are considered null;

From the values found we can make interesting remarks:

The first Ohm's law is verifyed by the first conductors : costantana, as we can see from the graphic
the second Ohm's law can be confirmed with the two last cases considered; depending the resistance from the geometric characteristics of the conductor, doubling the length of the conductor (connecting in seire two spin of the same Ni-Cr composition) the resistance doubles :R=(2.8±0.2) become R=(6.1±0.3);
while doubling the section (connecting in parallel) the resistance is halved R=(1.4±0.1);
Also confronting two threads of Ni-Cr, of section 0.56 and 0.70, we can notice that the resistance of the smaller section is a little bigger then the other. Also in this case it's possible to notice a proportion.
the resistance of the conductors as costantana and Ni-Cr, are equivalent.