Question

an infinite number of capacitors , having capacities 1, 2 ,4 , 8 micro farad are connected in series . the equi. capacitance of system is ...

Answer 1

An infinite number of capacitor are kept in series.. So
C equivalent = 1/c1 +1/c2 +1/c3 +1/c4.......
__________= 1 +1/2 +1/4 +1/8 +1/16.......
__________= 1/(1-½) = 1/½ =2 micro farad
.(since being in infinite gp series the sum can be done by a/(1-r) where a is initial value and r is the difference).

Hope I helped you.

Answer 2

equivalent capacitance of system is 0.5μF.

concept : equivalent capacitance of c1, c2, c3, c4, .... when all capacitors are joined in series combination is given by,

1/Ceq = 1/c1 + 1/c2 + 1/c3 + 1/c4 + ......

here capacitance are ; 1, 2, 4, 8, 16 , ....... ∞ terms

so, 1/Ceq = 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + ..... ∞ terms

as it is clear that given terms are in geometric progression where first term is 1 and common ratio is 1/2.

using formula, S_∞ = a/(1 - r)

here, a = 1 and r = 1/2

so, 1/Ceq = 1/(1 - 1/2) = 1/(1/2) = 2

hence, Ceq = 0.5 μF

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