Question

A cylindrical capacitor has tow co-axial cylinders of length 20 cm and radii 1.5 cm and 1.6 cm. The outer cylinder is earthed and inner cylinder is given a charge `4 muC.` The capacitance of the system is (neglect end effect)
A. `2.8xx10^(-8)F`
B. `4.2xx10^(-14)F`
C. `1.7xx10^(-10)F`
D. `3.4xx10^(-12)F`

Answer 1

Correct Answer - C
Here length L = 20 cm `= 20 xx 10^(-2)m`
inner radius `r_(1) = 1.5 cm = 1.5 xx 10^(-2)m`
outer radius `r_(o) = 1.6 cm = 1.6 xx 10^(-2)m`
charge `q = 4 muC = 4 xx 10^(-6)C`
Capacitance ,
`C = (2pi epsi_(0)L)/(log_(e)((r_(o))/(r_(i)))) = (2pi epsi_(0)L)/(2.3 log_(10)((r_(o))/(r_(i))))= (2pi xx 8.85 xx 10^(-12) xx 20 xx 10^(-2))/(2.3 log_(10)((1.6 xx 10^(-2))/(1.5 xx 10^(-2)))) `
` = 1.7 xx 10^(-10)` F