Question

Resistivity is the inverse of___.
(a) Resistance
(b) Conductivity
(c) Capacitance
(d) Current density

Answer 1

In this question,we are going to use the basic concepts of current electricity are to be used and the factors on which resistance and current flowing through a material depends.

Complete step by step answer:
Resistance: The resistance of a conductor is the property by virtue of which it opposes the flow of charges through it. The more the resistance, the less is the current I for a given potential difference. It is equal to the ratio of the potential difference applied across the conductor to the current flowing through it. Thus
$R = \dfrac{V}{I}$
Factors affecting the resistance: At a constant temperature, the resistance of a conductor depends on the following factors:
(1) Length: The resistance R of a conductor is directly proportional to its length i.e,
$R \propto \ell$
(2) Area of cross-section: The resistance R of a uniform conductor is inversely proportional to its area of cross-section A, i.e.
$R \propto \dfrac{\ell }{A}$
(3) Nature of the material: The resistance of a conductor also depends on the nature of its material. For example, the resistance of a nichrome wire is 60 times that of a corner wire of equal length and area of cross-section.
Combining the above factors , we get
$R \propto \dfrac{\ell }{A}$ or $R = \rho \dfrac{\ell }{A}$
Where $\rho$ is the constant of proportionality called resistivity or specific resistance of the material of the conductor. It depends on the nature of the material of the conductor and on the physical conditions like temperature and pressure but it is independent of its size or shape.
Resistivity or specific resistance. If in the above equation, we take
$\ell$ = 1 unit and A = 1 square unit
then $R = \rho$
Thus, the resistivity or specific resistance of a material may be defined as the resistance of a conductor of that material, having unit length and unit area of cross-section. Or, it is the resistance offered by the unit cube of the material of a conductor.
Current density: The current density at any point inside a conductor is defined as the amount of charge flowing per second through a unit area held normal to the direction of the flow of charge at that point. It is a vector quantity having the same direction as that of the motion of the positive charge. It is a characteristic property of any point inside the conductor and is denoted by $\overrightarrow j$ .
If a current I is flowing uniformly and normally through an area of cross section A of a conductor, then the magnitude of current density at any point of this cross-section will be
$j = \dfrac{{\dfrac{q}{t}}}{A} = \dfrac{I}{A}$
Conductivity. The reciprocal of the resistivity of a material is called its conductivity and is denoted by $\sigma$ .
Thus,
$Conductivity = \dfrac{1}{{\operatorname{Re} sistivity}}$
$\sigma = \dfrac{1}{\rho }$
$Capacitance = \dfrac{{Ch\arg e}}{{Potential}}$
Capacitance of a conductor may be defined as the charge required to increase the potential of the conductor by unit amount.
The capacitance of a conductor is the measure of its capacity to hold a large amount of charge without running a high potential. It depends upon the following factors:
1. Size and shape of the conductor.
2. Nature (permittivity) of the surrounding medium.
3. Presence of the other conductors in its neighbourhood.
From above it is clear that resistivity is the inverse of conductivity.
Hence, option (B) is the correct option.

Note: Before applying this concept, one must know that resistivity and conductively depend upon type of material. The term conductivity is related with conduction that is flow of current while the term sensitivity is related with the term resistance that is hindrance in flow of current. Materials like iron are good conductors, that’s why they have high conductivity but low sensitivity.