Question

a metallic wire of resistance R is cut into 10 parts of equal length 2 pieces each are joined in series and then 5 such combination are joined in parallel what will be the effective resistance of the combination

Answer 1

resistance of 10 equal parts = 1/10R
resistance of two 1/10 parts joined in series = 1/5R
let equivalent resistance be Rp
1/Rp = 1/1/5R*5
1/Rp = 25R
Rp = 1/25R

Answer 2

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

1/R’=R/25