Question

We know resistance is given by the equation,
$R=\frac{\rho l}{A}$
So, for a resistor of a particular material, if the resistance is doubled, by what factor does $\rho$ change?

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

Answer 1

The correct option is B 1

$\rho$ is not directly proportional to R. In fact, it is the constant of proportionality in the equation. So ρ doesn’t change when R does. Only l and A change. (Assuming the material doesn’t change).
$\rho$ is a property of the material and it only changes when you change the material.
You can also change ρ changes by changing temperature. Think about why this happens!