Question

# Find the equivalent capacitance between A and B for this infinite circuit of capacitors.

A
(51)C2
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B
(5+1)C2
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C
(15)C2
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D
None of these
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Solution

## The correct option is A (√5−1)C2 You’ll see a lot of questions like these and they’re all solved in the same simple manner. Consider the infinite combination as a “collection”. If I add one more unit to it, it should be fine right? Because ∞+1=∞. Now the unit here is, So, if add this to the circuit, we simply have the same Ceq Now the circuit is pretty simple isn’t it? We have the same Ceq across A and B. Ceq=C+(11C+1Ceq) Ceq=C+CCeqC+Ceq CCeq+C2eq=C2+CCeq+CCeq C2eq+CCeq−C2=0 Ceq=−C±√C2+4C22 Ceq=−C±√5C2 Clearly Capacitance cannot be negative. So, taking only the positive root, Ceq=(√5−1)C2 .

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