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I am curious- I know that resistance doubles when length does, and that resistance would be halved if cross sectional area was doubled -

But is there such a case of special conditions where It would be possible to double the length (or just increase it) while keeping resistance constant?

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We know that, $\displaystyle R = \rho \,\frac{L}{A}$.

So we need the resistance to be constant, Therefore, $\rho\dfrac{L}{A} = \text{constant}$

or, $L\propto \dfrac{A}{\rho}$.

Now the material of the resistance should also be should also be the same, Hence, we get, $L \propto A$.

So to double the length of the resistance without changing the resistance its area of cross section must also be doubled. This means that the volume of the resistor would increase so we need to add more material to the resistor.

But if the area of cross section also remains constant then check out the next answer.

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  • $\begingroup$ Please someone edit the answer with proper mathematical notations and tell me how can I do it. $\endgroup$
    – Abhirup Adhikary
    Commented Feb 28, 2020 at 5:50
  • $\begingroup$ MathJax tutorial $\endgroup$
    – G. Smith
    Commented Feb 28, 2020 at 6:20
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Yes, if you have a superconductor. Twice zero resistance is still zero resistance.

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