Question

A capacitance of an air capacitor is $25\mu F$ the separation between the parallel plates is $8mm$. An aluminum plate of thickness $2mm$ thickness is introduced symmetrically between the plates. The new capacitance will be

• A. $10\mu F$
• B. $33.3\mu F$
• C. $44\mu F$
• D. $50\mu F$

Answer 1

Answer: (B)

$C_m=\frac{{\epsilon }_{0}A}{d-t+\frac{t}{K}}$
$C_0=\frac{{\epsilon }_{0}A}{d-t}(K=\infty$ for metals $)$
$C_0=\frac{{\epsilon }_{0}A}{d}$
$\frac{C_m}{C_0}=\frac{{\epsilon }_{0}A}{d-t}\times \frac{d}{{\epsilon }_{0}A}=\frac{d}{d-t}$
$\frac{C_m}{C_0}=\frac{8}{8-2}=\frac{8}{6}$
$C_m=25\times \frac{4}{3}$
$=33.3\mu F$