Ohm's Law

The fundamental law governing the flow of electric current was formulated by the German physicist Georg Simon Ohm and it is called Ohm's law. It states that the ratio of potential difference between two points of the circuit to the current flowing between these points is constant and it is called the resistance between these points.

Let's look at Fig.1.

Fig.1 A circuit for measuring the resistance of a conductor.

On Fig. 1 there is a rod connected to a battery by two pieces of wire. There is a voltmeter connected to the ends of the rod reading a potential difference V across the rod. The ammeter measures the current I flowing in the circuit. We can use different batteries, changing in this way the potential difference V and current I, but the ratio R

R = V / I (1) will be always the same.

This ratio is called resistance. The SI unit of resistance is the ohm (1 volt/1 ampere), and the Greek letter Ω is often used to represent ohms. You can rearrange Eq.1 into form V = R I (2) and read it: The potential difference between two points of a circuit is equal to the product of resistance between these points and a current in this circuit.

There is a small problem requiring explanation. The piece of metal wire can be called a conductor as well a resistor. What is the difference, if any, between a conductor and a resistor?

Any material which is good at conducting electric current can be called a conductor. Any material which conducts electricity can be also called a resistor, because, except for the special case of materials in a superconducting state, even the best conductor resists the flow of electric current.

The name conductor or resistor is given to a piece of wire depending on the role it plays in an electric circuit. If this wire is used to connect a small bulb, for example, to a battery – it is called a conductor. If the relatively long wire is used to decrease the current flowing in the circuit it is called a resistor.

There are special elements called resistors. They are constructed from materials which are very bad conductors. The question arises how to divide materials into good and bad conductors.

The parameter describing such properties of materials is called resistivity. From the experiment we know that

the resistance of the piece of conductor in the from of a rod is proportional to the length of this rod and inversely proportional to the area of its cross section. Therefore the resistance R of the rod from Fig.1 can be written in the form R = ρ L / S (3) where L is the length, S - area of cross section, and ρ, the coefficient of proportionality, is called resistivity.Solving this Eq.1 for ρ , we have ρ = R S /L (4) The unit for resistivity is, [ ρ ] = Ω m² / m = Ω m In other words the resistivity of a given material is the resistance of an element 1 m long and with a cross section of 1 square meter made from this material. The resistivity allows us to compare the ability of materials to conduct electric current.

Resistivity is a quantity analogous to the density of matter. You cannot say that iron has a larger mass than wood, because you can have a large block of wood with a mass much larger then the mass of tiny piece of iron. But if you make a block of 1 cubic centimeter from wood and iron then you can make such a comparison. Density is the mass of unit of volume of a given material.

Analogically resistivity is a resistance of the rod of standard dimensions made from a given material.

Values of resistivity for a few well known substances are given below.

Substance ρ / Ω m

silver 1.47x10^-8

copper 1.59x10^-8

gold 2.27x10^-8

aluminum 2.60x10^-8

iron 11.0x10^-8

platinum 11.0x10^-8

carbon 4x10^-5

silicon 3x10⁴

wood (about) 3x10⁸

glass (about) 1x10¹²

fused quartz 5x10¹⁷

Silver is the best conductor and copper only slightly worse. It is the reason why a home's electric installation is made from copper wires. Gold is used in places where oxidation could influence the contact between different elements of the circuit and this could result in the malfunctioning of these circuits. Substances with very high resistivity (> 10⁶Ω m ) are called insulators.

Email this article to friend