Electrical resistance and resistivity

ELECTRICAL RESISTANCE OF A CONDUCTOR

• The property of a conductor due to which it opposes the flow of current through it is called resistance.
• It is a measure of ease of flow of electric charge through a given material or restriction to the flow of electric charge within the electric circuit.

UNIT OF RESISTANCE

From Ohm’s law,

The SI unit of resistance is ohm.

GRAPH BETWEEN V AND I

GOOD CONDUCTORS, RESISTORS AND INSULATORS

• Good conductors: Those substances which have very low electrical resistance are called good conductors.
• Resistors: Those substances which comparatively high electrical resistance, are called resistors.
• Insulators: Those substances which have infinitely high electrical resistance are called insulators.

FACTORS AFFECTING THE RESISTANCE OF A CONDUCTOR

• Water flowing through a pipe is affected by the cross section of the pipe, length of the pipe and the material of the pipe.
• The electrical resistance of a conductor (or a wire) is analogous to water flow through a pipe.
• It depends on the following factors:
  • Length of the conductor(L),
  • Area of cross-section of the conductor (or thickness of the conductor),A
  • Nature of the material of the conductor, and
  • Temperature of the conductor.

RESISTIVITY

It is defined as the resistance offered by a cube of a material of side 1 m when current flow perpendicular to its opposite faces.

Resistivity is a measure of a material’s ability to resist the flow of electric current.

Materials with low value of resistivity are good conductors of electricity.
Since insulators resist electric current more than conductors, its resistivity is more.

UNIT OF RESISTIVITY

DEDUCTION OF RESISTIVITY

Resistivity could be deduced as follows:

(i) The resistance of a given conductor is directly proportional to its length. That is:

$R\propto 1 ...\left(1\right)$

(ii) The resistance of a given conductor is inversely proportional to its area of cross-section. That is:

$R \propto \frac{1}{A} ...\left(2\right)$

By combining the relations (1) and (2), we get:

$$\begin{gathered} R \propto \frac{1}{A} \\ or \\ R = \frac{\rho \times 1}{A} ...\left(3\right) \end{gathered}$$

$Resistivity, \rho = \frac{R \times A}{1} ...\left(4\right)$

RESISTIVITY OF MATERIALS

• Silver metal is the best conductor of electricity.
• The resistivity of alloys is much higher than those of the pure metals (from which they are made). Alloy having a high resistivity is nichrome.
• The resistivity of semi-conductors like silicon and germanium is in-between those of conductors and insulators.
• Semi-conductors are used for making solar cells and transistors
• Resistivity of a few materials are as below:

WHY ARE THE HEATING ELEMENTS OF ELECTRIC APPLIANCES MADE OF ALLOY?

Heating elements (or heating coils) of electrical heating appliances such as electric iron and toaster, etc., are made of an alloy rather than a pure metal because

(i) The resistivity of an alloy is much higher than that of pure metal, and

(ii) An alloy does not undergo oxidation (or burn) easily even at high
temperature. Nichrome alloy is used for making the heating elements of electrical appliances.