If a wire of resistance R, resistivity ñ "roe", length L, and cross sectional area A, had its length doubled and radius halved, what would be the ratio of R'/R. Where R' is the new resistance of the wire.

Question

I thought it would be 4 times R, giving the ratio of 4R:R'
However, I plugged theoretical numbers in to check and it did not match what I thought. Can someone please explain the ratio to me?

Answer 1

R1=ρ•L1/A1
R2= ρ•L2/A2= ρ•2•L1•2/A1=4• ρ•L1/A1=4•R1