Question

The capacity of a parallel plate capacitor with no dielectric substance but with a separation of $0.4 \,cm$ is $ 2\mu F. $ the separation is reduced to half and it is filled with a dielectric substance of value of $2.8.$ The final capacity of capacitor is :

• A. $15.6 \, \mu F $
• B. $11.2 \,\mu F $
• C. $19\, \mu F $
• D. $22.4 \, \mu F $

Answer 1

Answer: (B)

$C=\frac{\varepsilon_{0} A}{d} \propto \frac{1}{d}$
Hence, $\frac{C_{1}}{C_{2}}=\frac{d_{2}}{d_{1}}$
or $\frac{2}{C_{2}}=\frac{0.2}{0.4}$
or $C_{2}=\frac{0.4 \times 2}{0.2}=4 \mu F$
Final capacity is
$C=4 \times k=4 \times 28$
$=11.2 \,\mu F$