NEET-XII-Physics
31: Capacitors
- #3Suppose, 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?Ans : The capacitance of a parallel-plate capacitor is given by
`` C=\frac{{\in }_{0}A}{d}``
Here,
A = Area of the plate
d = Distance between the parallel plates
Now,
Let the radius of the disc be r.
`` \therefore C=\frac{{\in }_{0}A}{d}=\frac{{\in }_{0}\left(\,\mathrm{\,\pi \,}{r}^{2}\right)}{d}``
`` \Rightarrow r=\sqrt{\frac{Cd}{{\in }_{0}\,\mathrm{\,\pi \,}}}``
`` \Rightarrow r=\sqrt{\frac{1\times (1\times {10}^{-3})}{8.85\times {10}^{-12}\times 3.14}}=\sqrt{35.98\times {10}^{6}}\,\mathrm{\,m\,}``
`` ``
`` \Rightarrow r\approx \sqrt{36\times {10}^{6}}\,\mathrm{\,m\,}=6\times {10}^{3}\,\mathrm{\,m\,}=6\,\mathrm{\,km\,}``
`` ``
Thus, the radius of the plates of the capacitor for the given configuration is 6 km.
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