Question

The effective capacitance between A and B of an infinite chain of capacitors joined as shown in the figure-

• A. ($\sqrt{3}$ – 1) mF
• B. $\frac{(\sqrt{5}–1)}{2}$mF
• C. ($\sqrt{5}$ – 1) mF
• D. 1 mF

Answer 1

Answer: (C)

($\sqrt{5}$ – 1) mF

Answer 2

= C_eq Ž C² + CC_eq = 2CC_eq + C_eq²

C_eq² +CC_eq – C² = 0 Ž C_eq = $\frac { - \mathrm { C } \pm \sqrt { \mathrm { C } ^ { 2 } + 4 \mathrm { C } ^ { 2 } } } { 2 }$

= $\left( \frac { \sqrt { 5 } - 1 } { 2 } \right)$ C