Question

True False Suppose I have a resistor of some resistance R. If I were to double the length and double the cross-sectional area of the resistor, what is the new resistance?

Answer 1

Explanation:

The resistance of a wire is given by :

$R=\rho\dfrac{l}{A}$

Where

$\rho$ is the resistivity of the wire

l = initial length of the wire

A = initial area of cross section

If length and the area of cross section of the wire is doubled then new length is l' and A', l' = 2 l and A' = 2 A

So, new resistance of the wire is given by :

$R'=\rho\dfrac{l'}{A'}$

$R'=\rho\dfrac{l}{A}$

R' = R

So, the resistance of the wire remains the same on doubling the length and the area of wire.