IIT JEE , AIEEE Forum - Physics , Electricity - the infinite grid again..i dont want the solution as whole..i want to be taught something

bvsatyaram

Hello Biki,

I understand ur confusion.

First to get started, let me make the principle of super position more clear.

In principle of super position, u take 2 things happening independently. (1 thing is independent of other. Any of these can exist without the existance of the other.).
U just take only first thing, observe the effect. Now take only second thing observe.
Principle of superposition says, the observation u make due to existence of both will be sum of the observations u make due existence of each of the things alone.

Now, lets get started.....
take the grid, trow in a current 4i into the grid at any grid point. (remember we are not goin to collect this current from the adjacent grid point.).Since the grid is symmetric, current divides equally that is., i, i, i, i.
Now, take a different case, take out current 4i from any grid point. (once agoin, we are not inputting current any where). So, what ever current u draw, has to be collected symmetrically. So, i, i, i, i.
Now club these 2 cases, so I am sending current 4i through A and collect 4i through B.

Forget about V and -V u were talking about. The current passing through wire B is 2i. So, potential difference accross A and B is 2i *r

Now, let the equivalent resistence be R.

So, replace the whole grid by a resistance R between A and B.
I am sending current 4i at one end and collecting the same current from the other end. (now there is no more grid, so, dont think about i,i,i,i and i. Just think abt outside 4i). So the potential difference accross A and B is R*4i
Therefore, 4i*R=2i*r
which implies R = r/2

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