Question

What is the capacitance of a parallel plate capacitor having $40\text{cm}\times 40\text{cm}$ square plates separated by the distance $10\text{cm}$?
(Take ${ϵ}_o=8.85\times {10}^{-12}\text{F/m}$)

• A. $2.8\times {10}^{-12}\text{F}$
• B. $1.4\times {10}^{-11}\text{F}$
• C. $2.8\times {10}^{-11}\text{F}$
• D. $1.4\times {10}^{-12}\text{F}$

Answer 1

The correct option is B $1.4\times {10}^{-11}\text{F}$

Area of each plate will be

$A=40\times 40{\text{cm}}^2=1600{\text{cm}}^2$

$\Rightarrow A=0.16{\text{m}}^2$

Distance between the plates

$d=10\text{cm}=0.1\text{m}$

When no medium is mentioned explicitly, assume air as the medium.

Now using formula of capacitance of parallel plate capacitor

$C=\frac{A{ϵ}_0}{d}$

$\Rightarrow C=\frac{0.16\times 8.85\times {10}^{-12}}{0.1}$

$\Rightarrow C=1.4\times {10}^{-11}\text{F}$

Hence, option $\left(b\right)$ is correct.