Question

Choose the correct answer from the alternatives given.
A capacitor made of two circular plates each of radius 12 cm and separated by 5 mm. The capacitor is being charged by an external source. The charging current is constant and equal to 0.15 A. The capacitance of the parallel plate capacitor is:

• A. 40 pF
• B. 45 pF
• C. 70 pF
• D. 80 pF

Answer 1

The correct option is D 80 pF

Given:

The radius of the circular plates is, $R=12cm=0.12m$

The distance between the two plates is, $d=5mm=5\times {10}^{-3}m$

To find: The capacitance of the parallel plate capacitor.

The area of the parallel plates is:

$A=\pi R^2$

$=3.14\times (0.12{)}^2{m}^2$

$=4.5\times {10}^{-2}{m}^2$

The capacitance of the parallel plate capacitor is given by:

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

$⟹C=\frac{8.85\times {10}^{-12}\times 4.5\times {10}^{-2}}{5\times {10}^{-3}}$

$=79.65\times {10}^{-12}=80pF$

Option $\left(D\right)$ is correct.