Find the equivalent resistance of the circuit between term inals A and B as dron shown in the figure below :

Explanation

Let the net resistance of the infinite circuit be X. Since network is definite, so one more set of resistances `2Omega, 3Omega and 4Omega` will not effect the resistance X of the network. So equivalent circuit can be drawn as:

Now resistances `3Omega and X` are in parallel and let their net resistance be `R_p`.
`:. 1/R_P=1/3+1/X=(X+3)/(3X)`
`R_P = (3X)/(3+X)`
Now resistances `2Omega, R_P and 4Omega` are in series.
So total resistance across A and B = R = 2 `+ R_p + 4`
` R = 6 +(3X)/(3+X)`
But as the total resistance of circuit remains uneffected.
`:. R = X`
`implies 6+(3X)/(3+X)=X`
`implies 16+6X +3Xs = 3X +X^2`
`implies X^2 - 6X -18=0`
On solving we get `X= 8.2 Omega`