IIT JEE , AIEEE Forum - Physics , Electricity

pink_ele

here ,

make those ends where curren t simply flows be free den

if pointing end of each circle is free

thus

in infinite sereis

one resistance doesnt effect

therefore

if x is eq resistance

n r is resistace of one side den

in parralel

1/r 1=1/(x)+1/(r)

r1=rx/(r+x)

now in series

r2=rx/(r+x)+r=2rx+r ²/(r+x)

finally taking parralel for final side n thus d eq resistance

1/x=(r+x)/2rx+r ²+1/r=3x+2r/(2rx+r ²)

thus solving

x=r/3

hope its correct