A Cylindrical Capacitor is Constructed Using Two Coaxial Cylinders of the Same Length 10 Cm and of Radii 2 Mm and 4 Mm. (A) Calculate the Capacitance. (B) Another Capacitor of the Same Length - Physics

Sum

A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.

Solution

(a) The capacitance of a cylindrical capacitor is given by C = (2pi∈_0l)/(In(R_2/R_1)

⇒ C = (2 xx 3.14 xx 8.85 xx 10^-12 xx 0.10)/("In"  2)

⇒ C = 8  "pF" (∵ "In"  2 = 0.693)

(b) When a capacitor of the same height with cylinders of radii 4 mm and 8 mm is taken, its capacitance comes to 8 pF, which is the same as above because the ratio of the radii is the same.

Concept: Capacitors and Capacitance
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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 9 Capacitors
Q 18 | Page 166