A capacitance of `2 muF` is required in an electrical circuit across a potential difference of `1.0 kV` A large number of `1 muF` capacitors are available which can withstand a potential difference of not more than `300 v`.
The minimum number of capacitors required to achieve this is

Options

A. 32
B. 2
C. 16
D. 24

Answer

A

Explanation

Let us assume that we connect n (whole number) capacitors in series such that the potential difference across the combination is 1000 V. This means the potential difference across each capacitor is
`V _("capacitor") = (1000)/(n) V le 300 V`
`n ge (1000)/(300) =3.333...`
`n _(min) = 4`
This means we need to connect at least 4 capacitors in series to make sure that the potential across each one is less than 300 V.
`C _(eq) = (m)/(n) C = 2mu F`
`(m)/(4) = 2`
`implies m = 8`
`therefore` Minimum no. of capacitors
`= 8 xx 4 = 32`