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An electric technician requires a capaci...

An electric technician requires a capacitance of `2muF` in a circuit across a potential difference of 1kV. A large number of `1muF` capacitors are available to him each of which can withstand a potential difference of not more than 400V. Suggest a possible arrangement that requires the minimum number of capacitors.

Text Solution

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Let a combination of capacitors be arranged in which m rows with n capacitors each are connected in parallel.
`:. 400n = 1000" "[:.1kV= 1000 V]`
or, `n = (1000)/(400) = 2.5 approx 3`
The equivalent capacitance of each row
`C = (1)/((1)/(1)+(1)/(1)+(1)/(1))muF = (1)/(3)muF`
The equivalent capacitance of m such connected in parallel shoukd be `2muF`.
But `C_(eq) = mC :. m = (C_(eq))/(C )= (2)/(1/3)=6`
Total number of capacitors `= 3xx6 = 18`
They should be arranged in 6 rows having 3 in each row and connected in parallel.
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