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