Question

A metallic wire of resistance R is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. What will be the effective resistance of the combination?

Answer 1

The resistance of a conductor is directly proportional to the length of the conductor. The resistance of the metallic wire, when it is cut into ten parts of equal length is

r=R/10

Two such pieces when  joined  in series, the equivalent resistance of these two parts

=r+r=2r=2R/10

Series resistance of two parts=2xR/10=R/5,

5 such elements are connected in parallel. Therefore the total resistance R' will be