Question

A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.

Answer 1

(a) The cylindrical capacitor’s capacitance is 0.8 pF.

(b) When there is a construction of another capacitor with the same length with cylinders of radii 8 mm and 4 mm, then the capacitance is 8 pF.

Explanation:

(a) A cylindrical capacitor’s capacitance is provided by the equation$\mathrm{C}=2 \pi \in \mathrm{O} \text { IInR } 2 \mathrm{R} 1$

$\Rightarrow \mathrm{C}=2 \times 8.85 \times 3.14(\text { pi value }) \times 10-12 \times 0.10 \ln 2$

$\Rightarrow C=8 \mathrm{pF}$

Therefore, ln $2=0.693$.

(b) A capacitor with the same height has the cylinders of radii 8 mm ad 4 mm. when it’s capacitance is calculated, it is found that it is 8 pF. This is same as that of (a). This is because the radii’s ratio is the same.