Question

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

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

Answer 1

Answer: (B)

Equivalent circuit of the given figure

Capacitance of capacitor $AB$,
$C=\frac{{\epsilon }_{0}A}{d}$
$=\frac{8.854\times 10^{-12}\times 50\times 10^{-4}}{3\times 10^{-3}}$
$=14.75\times 10^{-12}$
$C=\frac{8.854\times 10^{-12}\times 50\times 10^{-4}}{6\times 10^{-3}}$
$=7.36\times 10^{-12}$
Energy stored $=\left(\frac{1}{2}C{V}_1^2\right)+\frac{1}{2}C{V}_2^2$
$=\frac{1}{2}\left[14.75+7.36\right]\times 144\times 10^{-12}$
$=22.11\times 72\times 10^{-12}$
$=1.59\times 10^{-9}$
$=1.6nJ$