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 ?

A piece of wire having a resistance R is cut into five equal parts. a

1.	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 ?
Answer» Solution :(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`