Seven capacitors each of capacitance `2muF` are to be connected in a configuration to obtain an effective capacitance of `(10/11)muF`. Which of the combination (s) shown in figure will achieve the desired result?

Explanation

Suppose a parallel combition of n capacitors is connected in series with a series with a series combition of `(7-n)` capacitors.
Capacitance of paralllel combination,
`C_(1) = 2n muF`
Capacitance at `(7-n)` series, and
`C_(s) = (10)/(11) muF`, therefore, form
`(1)/(C_(s)) = (1)/(C_(1)) + (1)/(C_(2)) + (1)/(2n) + (7-n)/(2) = (11)/(10)`
Multiplying both sides by 10n, we get
`5+5n (7-n) = 11n`
`5+35n-5 n^(2) = 11n`
or `5 n^(2) - 24n - 5 = 0`
`(n-5) (5n + 1) = 0`
Rejecting parallel combination of 5 capacitors must be connected in series with combination of 2 capacitors.