Question

Suppose you have three resistors of 20 Ω, 50 Ω and 100 Ω. What minimum and maximum resistance can you obtain from these resistors?

Answer 1

maximum=20+50+100

=170ohm

minimum=(1/20+1/50+1/100)^-1

=100/8

=12.5ohm

Answer 2

Given,

Suppose you have three resistors of 20 Ω, 50 Ω and 100 Ω.

To find: What minimum and maximum resistance can you obtain from these resistors?

Solution:

Let the resistors be R1 =  20 Ω,R2= 50 Ω and R3=100 Ω.

For maximum resistance, all resistance must be in series

R(max) = R1 + R2 + R3

or, R(max) = 20 + 50 + 100

or, R(max) = 170

For minimum resistance, all resistance must be in parallel.

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

1 / R(min) = 1/20 + 1/50 + 1/00

or, 1 / R(min) = (5+2+1) / 100

or, R(min) = 100 / 8

Or, R(min) = 12.5 Ω