Question

Compared to the previous measurement at L=24cm, in this measurement, the only change is that the rod diameter decreased by a factor of two. Thus the area increases/decreases (circle one) by a factor of _ and thus the resistance should increase/decrease by a factor of _. Explain why with formula.

Answer 1

Resistance is given by:

R = rho*L/A

where rho is the resistivity, L is the length and A is the area = pi*d²/4, (d is the diameter)

Thus R is inversely proportional to the square of the diameter d;

R -> 1/d²

While area is directly proportional to the square of the diameter d;

A -> d²

The diameter is decreased by a factor of 2, d' = d/2

So the area decreases by a factor of A' -> (1/2)² = 0.25

and

Resistanceshould increase by a factor of R -> 1/(1/2)² = 4