A condenser is composed of 200 circular tin plates placed one after the other. The consecutive plates are separated by 0.5 mm thick mica sheets of dielectric constant 6. If the alternate tin plates are connected and the capacitance of the entire condenser is `0.4 muF`, what is the radius of each tin plate?

Explanation

The condenser is composed of 200 circular plates and alternate plates are connected. So, here we get 199 identical capacitors connected in parallel. Now capacitance of each capacitors is,
`C = (k alpha)/(4 pi d)= (k pi r^2)/(4 pi d)= (k r^2)/(4d)`
`:. " "(k r^2)/(4d)xx199 = 0.4xx 10^(-6)xx9xx10^(11)`
`[:. 0.4 muF = 0.4xx10^(-6)F " and "1F = 9xx10^(11) statF]`
or, `(6r^2)/(4xx0.05)xx199= 3.6xx10^(5)`
or, `r^2= (3.6xx10^(5)xx4xx0.05)/(6xx199)`
or, `r^2 = 60.3 " or, "r = 7.76`
So, the radius of each tin plate = 7.76 cm.