Question

The potential difference across a resistor is doubled. Its resistance changes by a factor of?(Assuming it’s an Ohmic conductor)

• A. 2
• B. $\frac{1}{2}$
• C. 1
• D. 4

Answer 1

The correct option is C 1

Resistance of any conductor depends on its resistivity $\left(\rho \right)$, length (l) and area of cross-section (A).
$R=\rho \frac{l}{A}$
Resistivity is the property of material and doesn’t depend on external factors like potential difference etc. (depends on temperature though)
Rest l and A has obviously no dependence on potential difference. So the resistance doesn’t change or rather “changes by factor of 1” (same thing)
You may think it like $R=\frac{V}{I}$ so as V changes R should change!!???
But yeah, NO!! That’s because as V changes, I also changes linearly with it (assuming the conductor to be Ohmic) so as to make the net change zero.