Question

A thick wire has ………… resistance than a thin wire.

Answer 1

The resistance of a wire generally resists the motion of electrons. So, intuitively, the thick wire can accommodate more free electrons than a thinner one. Typically, the cross-section area of a wire is inversely related to the resistance.

Formula used:
The resistance $R$ of a wire with length $l$ and cross-section area $A$ is
$R = \rho \dfrac{l}{A}$ ………..(1)
where $\rho$ is the of the material with which the wire is made.

Complete step by step answer:
Step 1:
Let the thicker wire has length $l$ and cross-section area $A$ and the thinner wire has the same length $l$ but the cross-section area $A{'}$, such that
$A{'} < A$

Step 2:
If the material for the two wires is the same, then calculate the resistance of the wires from eq (1).
The resistance of the thinner wire is
${R_{thin}} = \rho \dfrac{l}{{A{'}}}$
The resistance for the thicker wire is
${R_{thick}} = \rho \dfrac{l}{A}$

Step 3:
Now compare the two resistances.
$\dfrac{{{R_{thick}}}}{{{R_{thin}}}} = \dfrac{{\rho \dfrac{l}{A}}}{{\rho \dfrac{l}{{A{'}}}}}$
$\Rightarrow \dfrac{{{R_{thick}}}}{{{R_{thin}}}} = \dfrac{{A{'}}}{A}$
we know that, $A{'} < A$, hence, ${R_{thick}} < {R_{thin}}$.

$\therefore$ A thick wire has less resistance than a thin wire.

Note:
This problem also can be solved with a strong argument without getting into the expressions. In wires, the resistance arises due to the collisions or other preventions of the flow of electrons. For a thick wire and a thin wire in similar conditions of length and material, the thinner wire can accommodate fewer electrons to carry the current, while the thicker wire can accommodate more in number. So ultimately, the resistance to the flow of electrons would be much lesser in the thicker wire than in the thinner wire. Hence, you can see the inversely proportional relationship between resistance and the area of the cross-section of the wire.