Electrostatics Question 576
Question: 100 capacitors each having a capacity of $ 10\mu F $ are connected in parallel and are charged by a potential difference of $ 100kV $ . The energy stored in the capacitors and the cost of charging them, if electrical energy costs $ 108\ paise\ per\ kWh $ , will be [MP PET 1996; DPMT 2001]
Options:
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 $
Show Answer
Answer:
Correct Answer: C
Solution:
Energy stored in the capacitor $ =\frac{1}{2}CV^{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{108Paise}{3.6\times 10^{6}J} $ \Total cost of charging $ =\frac{5\times 10^{6}\times 108}{3.6\times 10^{6}}=150Paise $
