Question

A number of capacitors each of capacitance $1\mu \text{F}$ and each one of which gets damaged if the potential difference just exceeding $500\text{V}$ is applied. Then an arrangement suitable for giving a capacitor of capacitance $3\mu \text{F}$ across which $2000\text{V}$ may be applied, requires at least _____ capacitors. (Give integer value)

Answer 1

Number of capacitors possible in a series combination is,

$N_s=\frac{\text{Total voltage}}{\text{Max voltage it can with stand}}=\frac{2000}{500}$

$\therefore N_S=4$

There are $n$ such combinations are possible,

$\frac{N_{p}C}{N_s}=C_{\text{resultant}}$

$\frac{N_p\times 1\times {10}^{-6}}{4}=3\times {10}^{-6}$

$N_p=12$

[ Where $N_p$ is the number of parallel combination is possible]

The least number of capacitors required is,

$N=N_s\times N_p$

$=4\times 12$

$N=48$

Accepted answer : $48$