find resistance between a & b?

is it  

consider d resistance betwn a nd b as r

as itz a infinte loop d resistance for all d others after first loop is considered same as r

thus c 2 R's and one r .. are in series thus their equivalent resistance is (2R+r)

this equivalent resistance is in paralell wid R thus u get

1/r=1/R+1/(2R+r)

solvin this u get a quadratic equation and then solve it for d answer ..........

That is simple

Let Assume consider that the equivalent resistance b/w a and b = R_eq

Since there are infinite such loops thus consider the first three (3) resistors in combination with rest of the loops i.e. R_eq

Thus

(R_eq + R + R) II R= R_eq

or (R_eq + 2R ).R/ (R_eq+ 3R) = R_eq

 

solve to get R_eq

 

it is R[(root3) - 1] / 2

infinite resistance:-

Req=(Req+2R).R/(Req+3R)

 resiSTANCE ALONB  a nd b = Req

WE GET A QUADRATIC EQUATION LIKE THIS

Req^2+3R.Req-2R^2=0

Req=R()/2           ANSWER