A cylindrical capacitor is built using two coaxial cylinders, each having a length of 10 cm , and with radii of 2 mm and 4 mm . Determine the capacitance.

Correct answer: C. 8 pF The capacitance of a cylindrical capacitor is given by: C = (2 π _0 L)/( ((b)/(a))) Given L = 10 cm = 0.1 m , a = 2 mm , and b = 4 mm . Substituting the values: C = (0.1)/((18 × 10^9) ((4)/(2))) C = (0.1)/(18 × 10^9 × 2) Using 2 0.693 : C = (0.1)/(18 × 10^9 × 0.693) C = (0.1)/(12.474 × 10^9) C 8.01 × 10^ -12 F 8 pF

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Capacitors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Capacitors

A cylindrical capacitor is built using two coaxial cylinders, each...

A cylindrical capacitor is built using two coaxial cylinders, each having a length of

10 \text{ cm}

, and with radii of

2 \text{ mm}

and

4 \text{ mm}

. Determine the capacitance.

Options

A $2 \text{ pF}$
B $4 \text{ pF}$
C $8 \text{ pF}$
D $16 \text{ pF}$

Correct answer

C. $8 \text{ pF}$

Step-by-step solution

The capacitance of a cylindrical capacitor is given by:

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

Given

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

a = 2 \text{ mm}

, and

b = 4 \text{ mm}

.

Substituting the values:

C = \dfrac{0.1}{\left(18 \times 10^9\right) \ln\left(\dfrac{4}{2}\right)}

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

Using

\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}

C \approx 8.01 \times 10^{-12} \text{ F} \approx 8 \text{ pF}

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