A cylindrical capacitor is constructed using two coaxial cylinders, each having a length of 10 cm , and with radii of 4 mm and 8 mm . Calculate the capacitance.

Question

Quantrex Academy · Accepted Answer

Correct answer: D. 8 pF

The capacitance of a cylindrical capacitor is given by the formula:

C = \dfrac{2 \pi \epsilon_0 L}{\ln(b/a)}

Given:
Length

L = 10 \text{ cm} = 0.1 \text{ m}

Inner radius

a = 4 \text{ mm}

Outer radius

b = 8 \text{ mm}

Substituting the values into the formula:

C = \dfrac{2 \pi \epsilon_0 (0.1)}{\ln(8/4)}

Using

\dfrac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2

, we have

2 \pi \epsilon_0 = \dfrac{1}{18 \times 10^9} \text{ F/m}

.

C = \dfrac{0.1}{18 \times 10^9 \times \ln 2}

Since

\ln 2 \approx 0.693

:

C = \dfrac{0.1}{18 \times 10^9 \times 0.693}

C = \dfrac{0.1}{12.474 \times 10^9} \approx 8.01 \times 10^{-12} \text{ F}

C \approx 8 \text{ pF}

A cylindrical capacitor is constructed using two coaxial cylinders,...

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