Q.

You are given thirty two capacitors each having capacity 4 μF. How do you connect all of them to prepare a composite capacity having capacitance 8 μF?

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a

2 condensers in series and 16 such groups in parallel

b

8 condensers in series and 4 such groups in parallel

c

4 condensers in series and 8 such groups in parallel

d

all of them in series

answer is C.

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Detailed Solution

Let m condensers are joined in series and n such groups are in parallel.Capacity of m condensers connected in series1C′=1C1+1C2+…=mC or C′=Cm=4mWhen n such groups are connected in parallel, thenCeff=nC′=4nmGiven that Geff=8, ∴8=4nmOr     nm=2  or  n=2m                         ...(1)Further                 mn=32                           ....(2)Now    m×2m=32  or  m=4and     n = 2 x 4 = 8
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You are given thirty two capacitors each having capacity 4 μF. How do you connect all of them to prepare a composite capacity having capacitance 8 μF?