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Cylindrical Capacitor Formula

The capacitor is used to store large amounts of electric current in a small space. Capacitors include wide applications in electric juicers, electric motors, flour mills and other electrical instruments. The potential difference between each capacitor varies. There are many electrical circuits where capacitors are to be grouped accordingly to get the desired capacitance. There are two common modes including Capacitors in series and Capacitors in parallel. 

Cylindrical Capacitor

It is often used to store the electric charge. The Cylindrical capacitor is a type of capacitor that possess the shape of a cylinder having an inner radius as a and outer radius as b. 

Formula for cylindrical capacitor is 

CLCL = 2πkϵoln(b/a)2πkϵoln(b/a).

Where,

a =  inner radius of cylinder,

b = outer radius,

k = dielectric constant,

C/L = capacitance per unit length. 

Problem 1: A Cylindrical capacitor having a length of 8 cm is made of two concentric rings with an inner radius as 3 cm and outer radius as 6 cm. Find the capacitance of the capacitor. 

Answer: 

Given:

 Length L = 8 cm

 inner radius a = 3 cm

outer radius b = 6 cm 

Formula for cylindrical capacitor is

CLCL = 2πkϵoln(b/a)2πkϵoln(b/a).

Capacitance, C = L 2πkϵoln(b/a)2πkϵoln(b/a)

C = 8 ×× 10−2−2 m 2π×1×8.854×10−12F/mln(6/3)2π×1×8.854×10−12F/mln(6/3)

C = 6.42 ×× 10−10−10 F.

Capacitance of the capacitor = 6.42 ×× 10−10−10 F.

Problem 2: A cylindrical air capacitor consists of two concentric rings that have an inner radius of 4 cm and outer radius 7 cm. Find the capacitance per unit length.

Answer:

Given:

Inner radius a = 4 cm

outer radius b = 7 cm

Formula for cylindrical capacitor is

CLCL = 2πkϵoln(b/a)2πkϵoln(b/a)

 

          = 2π×1×8.854×10−12F/mln(4/7)2π×1×8.854×10−12F/mln(4/7) 

          = -9.94 ×× 10−11−11 F/m.

Capacitance per unit length =  -9.94 ×× 10−11−11 F/m.

 

 

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