Question

An isolated parallel plate capacitor is charged upto a certain potential difference. When a $3mm$ thick slab is introduced between the plates then in order to maintain the same potential difference, the distance between the plates is increased by $2.4mm$. Find the dielectric constant of the slab. (Assume charge remains constant)

• A. 5
• B. 10
• C. 2.5
• D. 7.5

Answer 1

Answer: (A)

$C_f=\frac{{\epsilon }_{0}A}{d^{\prime }-t(1-\frac{1}{K})}$
$C_i=C_f$
$\frac{{\epsilon }_{0}A}{d}=\frac{{\epsilon }_{0}A}{d^{\prime }-t(1-\frac{1}{K})}\Rightarrow d=d^{\prime }-t(1-\frac{1}{K})$
$d^{\prime }=d-2.4\times {10}^{-3}$
$t=3mm$
$d=d+(2\cdot 4\times {10}^{-3})-3\times {10}^{-3}(1-\frac{1}{K})$
$K=5$