Q. 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
A) $10^{7}\ joule$ and $300\ paise$
B) $5 \times 10^{6}\ joule$ and $300\ paise$
C) $5 \times 10^{6}\ joule$ and $150\ paise$
D) $10^{7}joule$ and $150\ paise$
Explanation
(c) Energy stored in the capacitor $= \frac{1}{2}CV^{2} \times 100$
$= \frac{1}{2} \times 10 \times 10^{- 6} \times \left( 100 \times 10^{3} \right)^{2} \times 100 = 5 \times 10^{6}\ J$
Electric energy costs $= 108\ paise\ per\ kWH = \frac{108\ Paise}{3.6 \times 10^{6}\ J}$
$\therefore$ Total cost of charging $= \frac{5 \times 10^{6} \times 108}{3.6 \times 10^{6}} = 150\ Paise$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.