Question

Three plates $A,B$ and $C$ each of area $50{cm}^2$, have a separation of $3mm$ between $A$ and $B$ and $3mm$ between $B$ and $C$. The energy stored when the plates are fully charged is :

• A. $6\times {10}^{-9}J$
• B. $3.12\times {10}^{-9}J$
• C. $2.12\times {10}^{-9}J$
• D. None of these

Answer 1

Answer: (C)

$2.12\times {10}^{-9}J$

Potential difference between A and B is $12V$.

Potential difference between B and C is also $12V$.

Now, $C=\frac{{ϵ}_{0}A}{d}=\frac{8.85\times {10}^{-12}\times (50\times {10}^{-4})}{3\times {10}^{-3}}=1.475\times {10}^{-11}$

$U_{AB}=U_{BC}=\frac{C{V}^2}{2}=\frac{1.475\times {10}^{-11}\times {12}^2}{2}=1.06\times {10}^{-9}$

Total energy stored,

$2\times 1.06\times {10}^{-9}=2.12\times {10}^{-9}$J