## 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 ε_{0(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 *ε_{0(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

ε_{0} → 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 ε_{0} 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 ε_{0} 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