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Question
Suppose, one wishes to construct a 1⋅0 farad capacitor using circular discs. If the separation between the discs be kept at 1⋅0 mm, what would be the radius of the discs?
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Solution
The capacitance of a parallel-plate capacitor is given by `C = (∈_0A)/d`
Here,
A = Area of the plate
d = Distance between the parallel plates
Now,
Let the radius of the disc be r.
`therefore C = (∈_0A)/d = (∈_0(pir^2))/d`
⇒ `r = sqrt((cd)/(∈_0pi)`
⇒ `r = sqrt((1 xx (1 xx 10^-3))/(8.85 xx 10^-12 xx 3.14))` = `sqrt(35.98 xx 10^6) "m"`
⇒ `r ≈ sqrt(36 xx 10^6) "m" = 6 xx 10^3 "m" = 6 "km"`
Thus, the radius of the plates of the capacitor for the given configuration is 6 km.
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