Question

A set of n-identical resistor each resistance R ohm when connected in series habe an effective resistance of ohm and when the resistor are connected in parallel the effective resistance is Yohm.find the relation between R,XandY?

Answer 1

When resistances are connected in series then
R=X1+X2+X3..........Xn.
Therefore total resistance is R=nX.
For parallel,
1/R=1/X1 +1/X2.........1/Xn
Therefore total resistance R=X/n.

Answer 2

Each resistance is of R

So in series
Effective resistance = X ohm = (R+R+R+R+....+ n times ) = Rn ohms

Now,
In parallel,
1/Effective resistance =1/Y = 1/R+1/R+1/R+.....+ ntimes = n/R
So,
Y = R/n
So, since we want a relationship between R X and Y

Thus let's multiply x and y

We get,

X*Y = nR*R/n = R^2

Therefore,
XY = R^2 will be the required answer.