Question

A cylindrical capacitor has a length of 1 cm and its inner cylindrical has a radius of 5cm. if the outer cylindrical has a radius of 50cm, what is the capacitance?​

Answer 1

Answer:

Length of a co-axial cylinder, l=15cm=0.15m

Radius of outer cylinder, r

1

=1.5cm=0.015m

Radius of inner cylinder, r

2

=1.4cm=0.014m

Charge on the inner cylinder, q= 3.5 µC

Capacitance of coaxial cylinder,

C=

ln(r

1

/r

2

)

2πε

o

l

=1.2×10

−10

F

Potential of the inner cylinder is given by,

V=

C

q

=2.92×10

4

V

Answer 2

Given: A cylindrical capacitor has a length of 1 cm, its inner radius is 5 cm and its outer radius is 50 cm

To find: Capacitance of this capacitor

Explanation: Length of capacitor(l)= 1 cm

= 0.1 m

Inner radius(a)= 5 cm

Outer radius(b)= 50 cm

The formula for calculating capacitance of cylindrical capacitor is:

=$\frac{2\pi \times 8.85 \times {10}^{ - 12 } \times l }{ ln( \frac{b}{a} ) }$

=$\frac{2 \times 3.14 \times 8.85 \times {10}^{ - 12} \times 0.1 }{ ln( \frac{50}{5} ) }$

=$\frac{5.56 \times {10}^{ - 12} }{ ln(10) }$

=$\frac{5.56 \times {10}^{ - 12} }{2.3}$ (since ln 10= 2.3)

=$2.41 \times {10}^{ - 12}$ F

Therefore, capacitance of the cylindrical capacitor is $2.41 \times {10}^{ - 12}$ Farad.