Question

What is the resistance RAB between the
terminals A and B of this infinitely repeating
chain of resistors.
Answer in units of Ω

Answer 1

please help ive bin trying to do this question for ages

Answer 2

remove the first part of the entire circuit,. let equivalent resistance be x..then add the removed part..the idea is that equivalent resistance stays the same,as number of resistors infinite,and removing one or adding makes no diff

Answer 3

sohail,first of all you let the equivalent resistance of the circuit between a and b be R.After this eliminate the part which is similar to infinite circuit which you have. and replace it by R resistance and you will get a simple circuit and find the equivalent resistance between a and b and put this equal to R. you will get a quadratic equation. solve this equation and find the value of R.....

Answer 4

thats what i said..........but frankly i find no use fir this infinite concept

Answer 5

Could you please elaborate?

Answer 6

the quadratic equation I get is x^2 -6.93 -56.4102

Answer 7

*6.93x

Answer 8

This question is very simple if you think of it this way:

Look at the first branch on the left. The lowest circuit resistance must be at least 2.8 + R + 4.13 ohms (series resistance). As you add parallel resistances across R, the total resistance of R (and its branches) will approach 0 ohms. It doesn't even matter what the resistances are on any of those parallel branches.

Therefore, the total circuit resistance if this ladder circuit went to infinity must be 6.93 ohms (since R will be 0 ohms at infinity).