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

Question

The effective capacitance between A and B of an infinite chain of capacitors joined as shown in the figure - <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-3rsyw7scm39id6pk.jpg" /> (A) (√3 - 1)C (B) ((√5 - 1)/2)C (C) (√5 - 1)C (D) C

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-3rsyw7scm39ikmtn.jpg" /> Ce q=(C (. C + Ce q .)/C + C + Ce q) = C2 + CCe q= 2CCe q + Ce q2 Ce q2+CCe q-C2 = 0 ⇒ Ce q = (- C ± √C2 + 4 C2/2) = ((√5 - 1/2))C

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

$(3 - 1) C$

$\frac{( 5 - 1 )}{2} C$

$(5 - 1) C$

$C$

$C_{e q} = \frac{C ( C + C _{e q} )}{C + C + C _{e q}}$
$= C^{2} + C C_{e q} = 2 C C_{e q} + C_{e q}^{2}$
$C_{e q}^{2} + C C_{e q} - C^{2} = 0 \Rightarrow C_{e q} = \frac{- C \pm C ^{2} + 4 C ^{2}}{2}$
$= (\frac{5 - 1}{2}) C$

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

(3​−1)C

2(5​−1)​C

(5​−1)C

C

Ceq​=C+C+Ceq​C(C+Ceq​)​ =C2+CCeq​=2CCeq​+Ceq2​ Ceq2​+CCeq​−C2=0⇒Ceq​=2−C±C2+4C2​​ =(25​−1​)C

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

$(3 - 1) C$

$\frac{( 5 - 1 )}{2} C$

$(5 - 1) C$

$C$

$C_{e q} = \frac{C ( C + C _{e q} )}{C + C + C _{e q}}$
$= C^{2} + C C_{e q} = 2 C C_{e q} + C_{e q}^{2}$
$C_{e q}^{2} + C C_{e q} - C^{2} = 0 \Rightarrow C_{e q} = \frac{- C \pm C ^{2} + 4 C ^{2}}{2}$
$= (\frac{5 - 1}{2}) C$