Question

A 100 meter long copper wire has a resistance of 100 Ω. Another copper wire has the same mass but is 10 meters long. Find the resistance of the second wire.Group of answer choices1 Ω10 Ω100 Ω1,000 Ω

Answer 1

Given that the length of the copper wire is l1 = 100 m and the resistance is R1 = 100 ohm.

We have to find the resistance of a copper wire when the length is l2 = 10 m

As we know that

$\begin{gathered} R1\propto l1 \\ R1=k(l1) \end{gathered}$

Let k be any constant.

Substituting the values, the k will be

$\begin{gathered} 100=k\times100 \\ k\text{ =}\frac{\text{100}}{100} \\ =\text{ 1 ohm- meter} \end{gathered}$

Now, the resistance in the wire will be

$\begin{gathered} R2=\text{ k}\times l2 \\ =1\times10 \\ =10\text{ ohm} \end{gathered}$