A set of n identical resistors, each of resistance `R Omega`, when connected in series have an effective resistance `X Omega` and when the resistors are connected in parallel, their effective resistance is `Y Omega`. Find the relation between R, X and Y.

Explanation

When n identical resistors are connected in series `X=R+R+R+ ..............+R=nR`
and r esistors are connected in parallel `(1)/(Y)=(1)/(R)+(1)/(R)+............+(1)/(R)=(1)/(R)=(n)/(R)rArrY=(R)/(n)`
`rArrX=nR=((R)/(Y))R=(R^(2))/(Y)therefore XY=R^(2)`