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Asked by Prashant DIGHE | 13 Mar, 2020, 22:14: PM
answered-by-expert Expert Answer
As seen from fig.1, due to infinite arrangment of capacitance,
we can consider if X is the effective capacitance across the point s A and B.
If capacitors which are left of points D and E are removed ,
then we will get same effective capacitance across points D and E..
 
Hence at fig.2, the infinite chain of capacitors right side of D and E is replaced with efective capacitance X.
 
Fig.3 shows the reduction so that parallel combination of capacitance of C and X is replaced by C+X.
 
Finally we get effextive capacitance from the relation  ,  (1/X) = (1/C) + [ 1/(C+X) ]
 
we get a quadratic equation from above equation as,  X2 + C X - C2 = 0
 
Above quadratic equation has solution, X = [ (√5 - 1 ) / 2 ] C
Answered by Thiyagarajan K | 13 Mar, 2020, 23:09: PM

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