A piece of wire having a resistance R is cut into five equal parts.
a) How will the resistance of each part of the wire change compared with the original resistance ?
b) If the five parts of the wire are placed in parallel, how will the resistance of the combination change ?
c) What will be the ratio of the effective resistance in series connection to that of the parallel connection ?

Explanation

(a) Consider a pieces of wire having resistance R. It cut into 5 equal parts So number of equal resistros are 5.
`n=5`
When .n. resistors of equal resistance R are connected in series, the equivalent resistance is .nR.
`:.R_(s)=nR`
`R_(s)=5R`
`R=(R_(s))/(5)rArr R=0.2R_(s)`
Each part of resistance .R. is equal to 0.2 times of original resistance.
(b) Effective Resistance of 5 Resistors `(1)/(R_(p))=1/R+1/R+1/R+1/R+1/R`
`=5/R`
`R_(p)=R/5=0.2R`
`R_(p)=0.2R`
(c ) Effective resistance of series combination `R_(S)=5R`
Effective resistance of parallel combination `R_(P)=(R)/(5)`
The ratoi series connection to the parallel connection `(R_(S))/(R_(P))=(5R)/((R//5))`
`(2)(9-R_(2)+R_(2))=(9-R_(2))R_(2)`
`(R_(S))/(R_(P))=5Rxx(5)/(R)`
`=25`
`R_(S):R_(P)=25:1`