Question

Three plates $ A, B $ and $ C $ each of area $ 50\, cm^2 $ have separation $ 3 \,mm $ between $ A $ and $ B $ and $ 6 \,mm $ between $ B $ and $ C $ . The energy stored when the plates are fully charged by a $ 12\, v $ battery is

• A. $ 2\,\mu J $
• B. $ 1.6\,n J $
• C. $ 5\,\mu J $
• D. $ 3.2\,n J $

Answer 1

Answer: (B)

Equivalent circuit of the given figure

Capacitance of capacitor $AB$,
$C = \frac{\varepsilon_{0}A}{d} $
$ = \frac{8.854\times 10^{-12} \times 50 \times 10^{-4}}{3\times 10^{-3}} $
$ = 14.75 \times 10^{-12} $
$ C = \frac{ 8.854 \times 10^{-12} \times 50 \times 10^{-4}}{6\times 10^{-3}} $
$ = 7.36 \times 10^{-12} $
Energy stored $= \left(\frac{1}{2} CV_{1}^{2}\right) + \frac{1}{2}CV_{2}^{2}$
$ = \frac{1}{2}\left[14.75 + 7.36\right]\times144\times 10^{-12}$
$ = 22.11 \times 72 \times 10^{-12} $
$= 1.59 \times 10^{-9} $
$ = 1.6 \,nJ$