#### 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.

Is there an error in this question or solution?

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.