A wire has length l, cross-sectional area a, resistivity p and resistance R. It is compressed to a third of its original length but its volume and resistivity are constant. Show its new resistance is R/9.
First realize if its length is now l/3 but its volume is constant its cross sectional area is 3a. Substitute those into the equation for resistance R=p(l/a) and you get (1/9)(p(l/a))= R/9
