Consider the following network of capacitors extended up to infinity. Find equivalent capacitance between P and Q.

Explanation

Let x be effective capacitance between P and Q then 2x must be the equivalent capacitance between R and S, as the capacitors, are doubled.
We can write the following equation for the above diagram:
`x=C+(4Cx)/(2C+2x) rArr x=(2C^(2)+2Cx+4Cx)/(2C+2x)`
`rArr 2Cx+2x^(2)=2C^(2)+2Cx+4Cx`
`rArr x^(2)-2Cx-C^(2)=0`
`rArr x=(2Cpm sqrt(4C^(2)+4C^(2)))/(2)=Cpm C sqrt(2)`
Selecting positive value for the answer we get equivalent capacitance `C(sqrt(2)+1)`.