Question

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

Answer 1

Hint
To answer this question, we have to use the relation of the resistance of a wire with its length and the cross sectional area. From there we can compare the resistance of a thick and a thin wire to find the final answer.
Formula Used: The formula which is used in solving this question is given by
$\Rightarrow R = \rho \dfrac{l}{A}$, here $R$ is the resistance of a wire, $l$ is its length, and $A$ is its area of cross section.

Complete step by step answer
We know that the relation of the resistance of a wire with the length and the cross sectional area is given by
$\Rightarrow R = \rho \dfrac{l}{A}$ (1)
If the diameter of the wire is $D$, then its area of the cross section is given by
$\Rightarrow A = \pi {\left( {\dfrac{D}{2}} \right)^2}$
That is,
$\Rightarrow A = \dfrac{{\pi {D^2}}}{4}$
Substituting this in (1) we get
$\Rightarrow R = \rho \dfrac{{4l}}{{\pi {D^2}}}$
Now if the resistivity and the length of the wire are constant, then the only variable in the above equation remains the diameter. Combining all the constants into a single constant $k$ in the above equation, we get
$\Rightarrow R = \dfrac{k}{{{D^2}}}$
So we have
$\Rightarrow R \propto \dfrac{1}{{{D^2}}}$
Thus the resistance of a wire is inversely proportional to the square of its diameter.
Now, we know that a thick wire has more diameter than a thin wire. So from the above proportionality we can easily conclude that a thick wire has a lower resistance than a thin wire.
Hence, the answer to this question is “low”.

Note
We must not be confused as to why the resistivity and the length of the wires are taken to be the same. While we are comparing a thicker wire with a thinner wire, we have to take its other parameters, apart from the diameter, as the same. Otherwise the change in the value of resistance will occur due to the change in other parameters also.