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

 

Let us assume that there are three resistors where each of their resistance is R ohm,

 

And it is given that when al the three resistors are connected in series their effective resistance is X ohm. And when connected in parallel, their effective resistance is Y.

 

Therefore the relation between R, X and Y is given below.

 

When connected in series, the effective resistance is given by

 

 

When conected in parallel, their effective resistance is