Cylindrical  capacitor Formula with Example

Cylindrical  capacitor Formula :

Cylindrical capacitor formula C(f) in farad  is  equal to the  two pi value π in3.14 multiply the Permittivity of free space ε0(f/m) in farad per meter and multiply length of the cylinder L(m) in meter division of In multiply the inner and outer radius cylinder a and b in centimeter. Hence the cylindrical capacitor formula can be written as

C(f) =2 π *ε0(f/m)* L(m) /ln(b(cm)/a(cm)

Where,

C→ capacitance of the cylinder in farad

L →length of the cylinder in meter

a → inner radius of the cylinder in cm

b → outer radius of the cylinder in cm

ε0 → Permittivity of free space (8.85 ×10-12) in Farad/meter

Sample Example :

Example 1:

Calculate the capacitance of the capacitor? In a Cylindrical capacitor having a length of 5 cm is made of two concentric rings with an inner radius of 4 cm and an outer radius of 3cm.

Solution :

Given,

Length L=5cm

Inner radius a=4cm

Outer radius b=3cm

The formula for the cylindrical capacitor is

C=2 π ε0 L /ln(b/a)

C=(2)(3.14) (8.85 ×10-12)(5×10-2)/ln(4/3)

C=2.7789 ×10-14 /0.2876

C=9.662 ×10-11 F

Example 2:

Calculate the capacitance of the capacitor? In a Cylindrical capacitor having a length of 10 cm is made of two concentric rings with an inner radius of 20 cm and an outer radius of 30cm.

Solution :

Given,

Length L=10cm

Inner radius a=20cm

Outer radius b=30cm

The formula for the cylindrical capacitor is

C=2 π ε0 L /ln(b/a)

C=(2)(3.14) (8.85 ×10-12)(10×10-2)/ln(30/20)

C=5.5578 ×10-14 /0.4055

C=1.3706 ×10-11 F

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