Question

Consider a parallel-plate capacitor of capacitance $10\mu F$ with air filled in the gap between the plates. Now, one half of the space between the plates is filled with a dielectric of dielectric constant 4 as shown in the figure. The capacitance of the capacitor changes to

• A. $25\mu F$
• B. $20\mu F$
• C. $20\mu F$
• D. $40\mu F$

Answer 1

The correct option is A $25\mu F$

From given we can redraw circuit as

$\begin{array}{cc}{C}_{eq}& =C_1^{\prime }+C_2^{\prime }\\ & =\frac{K{\epsilon }_0\frac{A}{2}}{d}+\frac{{\epsilon }_0\frac{A}{2}}{d}\\ & =\frac{K{\epsilon }_{0}A}{2d}+\frac{{\epsilon }_{0}A}{2d}\\ & =\frac{{\epsilon }_{0}A}{2d}[K+1]\end{array}$

From given $\frac{{\epsilon }_{0}A}{2d}=10\mu F$ and $K=4$.
On substituting these values
we get, $C_{eq}=25\mu F$