Question

Given three resistors each of resistors R. How will you combine them to get the
( i ) maximum
and (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?

Answer 1

Hi friend !!!!

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Given three resistors each of resistors R.To get the maximum effective resistance, you have to connect the resistors in series combination

effective resistance of a series combination =R1+R2+R3=R+R+R=3R

→To get the minimum effective resistance, the resistors should be connected in parallel series.

♦effective resistance of parallel combination = 1/(1/R1+1/R2+1/R3)=1/(1/R+1/R+1/R)=1/(3/R)=R/3

→Now,the ratio of the maximum to minimum resistance = (R1+R2+R3)/[ 1/(1/R1+1/R2+1/R3)]

=(R1+R2+R3)(1/R1+1/R2+1/R3)

=3R(3/R)=9:1

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I hope this will help u ;)

Answer 2

Hey there !!!

Resistance of given resistors =R

We get maximum resistance when these resistors are in a series connection.

R (equivalent)=R₁+R₂+R₃=R+R+R=3R

Maximum Resistance =3R.

Minimum Resistance is obtained when all 3 resistors are in parallel connection.

R(equivalent) in parallel connection for "n" equal resistances =R/n

So R(equivalent)=R/3

Minimum resistance=R/3

So R(max):R(min)=3R/R/3=9

R(max):R(min)=9:1