Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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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? - Physics

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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?

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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Solution 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? Concept: Capacitors and Capacitance.
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