Ohm's Law

INSTITUTO POLITÉCNICO NACIONAL
ESCUELA SUPERIOR DE CÓMPUTO

Circuits Fundamental Analysis Laboratory

Report 2
OHM's LAW


September 7th, 2012

INDEX

1.0 Ohm's law theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Circuit analysis . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Resistive circuits . . . . . . . . . . . . . . . . . . . . . . . . 41.3 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.0 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Voltage dependence . . . . . . . . . . . . . . . . . . . . . 6
2.2 Unit resistanse . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Calculating the power in the resistors . . . . . . . . 9

3.0 Conclusions . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.0 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

5.0 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

6.0 Anexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

OHM's LAW
1.0 Ohm's law states that the current through a conductorbetween two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is theresistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.
The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly morecomplex equation than the one above (see History section below) to explain his experimental results. The above equation is the modern form of Ohm's law.
In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

where J is the current density at a given location in a resistive material, E is the electricfield at that location, and σ is a material dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff.
1.1 Circuit analysis

In circuit analysis , three equivalent expressions of Ohm's law are used interchangeably:

Image 1.11 Ohm's law triangle

Each equation is quoted by some sources as the defining relationship of Ohm's law, or all threeare quoted, or derived from a proportional form, or even just the two that do not correspond to Ohm's original statement may sometimes be given.
The interchangeability of the equation may be represented by a triangle, where V ( voltage ) is placed on the top section, the I ( current ) is placed to the left section, and the R ( resistance ) is placed to the right. The line that divides the leftand right sections indicate multiplication, and the divider between the top and bottom sections indicates division (hence the division bar).
1.2 Resistive circuits
Resistors are circuit elements that impede the passage of electric charge in agreement with Ohm's law, and are designed to have a specific resistance value R . In a schematic diagram the resistor is shown as a zig-zag symbol. Anelement (resistor or conductor) that behaves according to Ohm's law over some operating range is referred to as an ohmic device (or an ohmic resistor ) because Ohm's law and a single value for the resistance suffice to describe the behavior of the device over that range.
Ohm's law holds for circuits containing only resistive elements (no capacitances or inductances) for all forms of driving voltage...