A student requires a capacitor of `3 muF` in a circuit across a potential of 1000 V. A large number of `2 muF` capacitors are available to him, each of which can withstand a potential difference of not more than 300 V. How should the student arrange these capacitors so that he may use minimum number of condensers ?

Explanation

Let the student use minimum number of N capacitors in m rows in parallel and n condensers in m rows in parallel and n conderers in series in each row.
`:. N = m xx n` …(i)
As each capacitor in a row can withstand 300 V, therefore, voltage across each row
`= 300 n = 1000V`
`n = (1000)/(300) = 3.3`
`:.` There should be four capacitors in each row.
Capacitance of each row
therefore, `C_(s) = (C )/(4) = (2)/(4) = 0.5 muF`
As m such rows are in parallel,
`m = (C')/(C_(s)) = (3 m,uF)/(0.5 muF) = 6`
From (i) , ` N = 6xx4 = 24`
This is the minimum number of capacitor required by the student.