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$100$ capacitors each having a capacity of $10\,\mu F$ are connected in parallel and are charged by a potential difference of $100\,kV$. The energy stored in the capacitors and the cost of charging them, if electrical energy costs $108\;paise\;per\;kWh$, will be
${10^7}\;joule$ and $300\;paise$
$5 \times {10^6}joule$ and $300\;paise$
$5 \times {10^6}joule$ and $150\;paise$
${10^7}\,joule$ and $150\;paise$
Solution
(c) Energy stored in the capacitor $ = \frac{1}{2}C{V^2} \times 100$
$ = \frac{1}{2} \times 10 \times {10^{^{ – 6}}} \times {(100 \times {10^3})^2} \times 100 = 5 \times {10^6}\,J$
Electric energy costs $ = 108\,Paise\,per\,kWH$$ = \frac{{108\,Paise}}{{3.6 \times {{10}^6}\,J}}$
Total cost of charging $ = \frac{{5 \times {{10}^6} \times 108}}{{3.6 \times {{10}^6}}}\, = 150\,Paise$
