A parallel plate capacitor with air between the plates has capacitance $12 \mu \mathrm{F}$. If the distance…

A parallel plate capacitor with air between the plates has capacitance $12 \mu \mathrm{F}$. If the distance between the plates is doubled and the space between the plates filled with a substance of dielectric constant 4 , the capacitance of the capacitor will be is
  1. $24 \mu \mathrm{F}$
  2. $72 \mu \mathrm{F}$
  3. $6 \mu \mathrm{F}$
  4. $12 \mu \mathrm{F}$

Solution

We have $\begin{aligned} & \mathrm{C}=\frac{\mathrm{KA} \varepsilon_0}{\mathrm{~d}} \\ & \mathrm{C} \propto \frac{\mathrm{K}}{\mathrm{d}} \\ & \mathrm{C}_2=\mathrm{C}_1 \times \frac{\mathrm{K}_2}{\mathrm{~K}_1} \times\left(\frac{\mathrm{d}_1}{\mathrm{~d}_2}\right) \Rightarrow \mathrm{C}_2=12 \times \frac{4}{1} \times \frac{1}{2}=24 \mu \mathrm{F}\end{aligned}$

Asked in: AP EAMCET 2022 (08 Jul Shift 1)

Practice more Electrostatics questions on Aicharya