Question

Name the factors on which the resistance of a wire depends. Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?

Answer 1

Hint: Resistance is the factor that affects the rate of flow of charges in a closed circuit. The measure of opposition that is offered by a material for the flow of current through it. Its SI unit is ohm ($\Omega $).

Complete step by step solution:
Since resistance is a measure of the opposition to the flow of electric current, we can say that the electric current and electric resistance are inversely proportional to each other. This fact is further justified by Ohm’s law which states $V = IR$. Therefore we can conclude that $I\alpha \dfrac{1}{R}$.

But what decides electric resistance? Does a given material have the same resistance irrespective of its shape and size? How does the resistance vary from one material to another?

Consider two wires A and B made of the same material and of length l and 2l respectively, and of same cross sectional area. Connect the two wires to the same source of voltage independently. Due to the applied potential difference, the electrons start moving through both the wires. Due to collisions, there will be resistance faced by the electrons throughout its motion. Since the electrons in wire A has to move less distance compared to that of electrons in wire B, we can say that resistance offered for electrons in wire A is less than that offered for electrons in wire B. Hence we can say that resistance is directly proportional to the length of the wire.

Now consider two wires C and D made of the same material and of cross sectional area A and 2A respectively, but of same length. Connect the two wires to the same source of voltage independently. The electrons have to travel the same distance here. But since the cross sectional area available for the wire C is less than wire D, we can say that the resistance offered for the flow of electrons in C is more than that in D. Hence we can conclude that the resistance is inversely proportional to the cross sectional area.

Now consider two wires E and F made of aluminium and copper respectively, but of same length and cross sectional area. Connect the two wires to the same source of voltage independently. When the electric current flowing through these wires are measured, it is found that current through copper is greater than that through aluminium. Here, since the nature of materials are different, the resistance offered for the flow of electrons will be different. Hence we can say that the resistance is directly proportional to the nature of the material.

Hence we can say that the resistance depends on the following factors:

1. Length of the wire
2. Cross sectional area of the wire
3. Nature of the material of the wire

Combining all these factors we get
$R = \dfrac{{\rho L}}{A}$
Where R is the electric resistance, ρ is the measure of electric nature of the material and is called as resistivity, L is the length of the wire and A is the cross sectional area of the wire.

When we consider two wires made of the same material and of same length but different thickness then the magnitude of current flowing through both these wires will be different.
Thicker wire offers lesser resistance compared to that of a thinner wire of same length and same material, connected to same source voltage.

Hence current through a thicker wire will flow more easily than that in a thinner wire of
same length and same material, connected to same source voltage.

Note: Resistivity is also known as specific resistance and its SI unit is $\Omega $m. When $L = 1m$and $A = 1{m^2}$we get $R = \rho $.
Resistivity varies from one material to another. Resistivity of a material varies in direct resonance with the temperature.
Resistance of two wires of different materials can be made to be the same. But resistivities of two materials can never be the same.