Question

What is electrical resistivity? In a series electrical circuit consisting of a resistor having a metallic wire, the ammeter reads $5A$ . The reading of the ammeter decreases to half when the length of the wire is doubled. Why?

Answer 1

Hint:In the problem, we have to define electrical sensitivity. Also, we are given that the reading of the ammeter decreases to half when the length of wire is doubled. We should know the formula of resistance in terms of resistivity of material, length of wire and area of cross section so as to solve the problem and find the dependency of the resistance over these factors.

Formulae used:
According to Ohm's law, at constant temperature, pressure and other physical affects the current flowing through the conductor is directly proportional to the potential drop between them.
$V\propto I$
$\Rightarrow V=RI$
where $R$ is proportionality constant called resistance.

Complete step by step answer:
The resistance of the conductor offers opposition to the flow of current. Resistance not only depends on the material of the conductor but also on the dimension of conductor.
$R\propto {\displaystyle \frac{l}{A}}$
$\Rightarrow R=\rho {\displaystyle \frac{l}{A}}$
where $\rho$ is a proportionality constant called resistivity.

The specific resistance of a material is equal to the resistance of the wire of that material with unit cross-section area and unit length.Resistivity depends on;
-Nature of material
-Temperature of material $\rho$ does not depend on the size and shape of the material because it is the characteristic property of the conductor material.

According to ohm’s law, resistance is inversely proportional to current if potential difference is constant. Also, resistance is directly proportional to the length of conductor.So, if the length of wire (conductor) is doubled, resistance also doubles. And if resistance is doubled, current becomes half.

Note:Resistivity is a property of a substance, whereas resistance is a property of an object. For example, density is a property of a substance, whereas mass is the property of an object. The unit of resistance is ohm denoted by $\mathrm{\Omega }$.The resistance of a conductor is said to be $1\mathrm{\Omega }$ if a current of $1A$ flows through it when the potential difference across its end is $1V$.