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

Resistance of a piece of wire is proportional to its length i.e. `R prop l`
Each piece has a resistance =R
Wire is cut into five equal parts
`therefore ` Resistance of each part `=R/5`
Resistance = `R/5`
b) All the five parts are connected in parallel.
For parallel connection , the effective resistance is
`1/(R_(p))=1/(R_(1)) + 1/(R_(2))`
`1/(R_(P))=5/R + 5/R + 5/R + 5/R R/R`
`1/(R_(P))=(25)/(R) implies therefore R_(P)=(R)/(25)`
The ratio of the effective resistance in series to paralle connection.
`1/(R_(P)) =(25)/(R_(s)) implies (R_(s))/(R_(P)) =(25)/(1)`
Ratio of `R_(1) & R_(P)=25:1`