An electrical technican requires a capacitance fo `2 muF` in a circuit across a potential difference of 1kV. A large number `1muF` capacitor 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.

Explanation

`C_("eff")=2muF= 2 xx 10^(-6)F " "V=1kV=10^(3)V" "C=1muF=10^(-6)F," rate 400V"`
Total change, `Q=C_("eff") V=2 xx 10^(-6) xx 10^(3)=2 xx 10^(3) C`
Let there be .n. capacitors in series and m such rows in the circuit.
Effective capacity, `C_("eff")=C/n xx m`
`2 xx 10^(-6) =(10^(-6)m)/(n)" m=2n"`
Also `(1000)/(n) lt 400 " i.e,"=(10)/n lt 4`
`5/n lt 2 or 2n lt 5, n gt 2.5 i.e, " 3 Hence m=6"`