Question

The capacity of a parallel plate condenser consisting of two plates each of $10c{m}^2$, separated by a distance of $2mm$ is:

(Take air as the medium between the plates)

• A. $8.85\times {10}^{-13}F$
• B. $4.42\times {10}^{-12}F$
• C. $44.25\times {10}^{-12}F$
• D. $88.5\times {10}^{-13}F$

Answer 1

The correct option is B $4.42\times {10}^{-12}F$

$\text{Step 1: Capacitance calculation}$ $\text{[Ref. Fig.]}$

Given,

Area $A=10c{m}^2=10\times ({10}^{-2}m{)}^2$ $={10}^{-3}{m}^2$

Air Gap $d=2mm=2\times {10}^{-3}m$

We know that Capacitance of a parallel plate capacitor is given by:

$C=\frac{{\in }_{0}A}{d}$

$=\frac{8.85\times {10}^{-12}\times \left({10}^{-3}{m}^2\right)}{2\times {10}^{-3}m}=4.42\times {10}^{-12}F$

Hence option (B) correct.