Question

There are n-resistor each of resistance R. Find the ratio of equivalent resistance in series to parallel combination.

please explain ​

Answer 1

Answer:

For maximum effective resistance, the resistors must be connected in series combination. If then are n resistors each of resistance R, then the maximum effective resistance =nR

For minimum effective resistance, the resistors must be connected in parallel combination.

So, the minimum effective resistance =

n

R

Ratio of the maximum to minimum resistance is

(R/n)

nR

=n

2

:1.

Answer 2

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Let’s assume each resistance to be x.

Now when connected in series,

(x+x+...ntimes)=R

or, nx=R

or x=Rn .

Now when connected in parallel,

1Req=(1Rn+1Rn+...ntimes)

or, 1Req=(nR+nR+...ntimes)

or, 1Req=n2R

or, Req=Rn2