Question

What is the capacitance of a pair of circular plates with a radius of 4.0 cm separated by 3.0 mm of mica?

Answer 1

The capacitance of a pair of a circular plates is(C) =8.90× 10⁻¹¹  F

How can we calculate the value of capacitance?

To calculate the value of the capacitance of a pair of a circular plates we are using the formula,

C= K$\frac{\epsilon_0 A}{d}$

Here we are given,

K= Dielectric constant of mica.

=6.

A= the area of the circular plates.

= $\pi$r²            

(Note: r is the radius of the circular plates

= 4.0 cm

= 0.04 m)

=  $\pi$× (0.04)²

$\epsilon_0$= permittivity of the vacuum

=  8.854×10⁻¹²  F⋅m⁻¹

d= Separating distance of the plates

=  3.0 mm

= 0.003 m

now we put the known values in the above equation, we get

C= K$\frac{\epsilon_0 A}{d}$

Or, C=$\frac{6\times 8.854\times 10^{-12}\times 3.14\times 0.04\times 0.04}{0.003}$

Or, C= 8.90× 10⁻¹¹ F

From the above calculation we can conclude that, The capacitance of a pair of a circular plates is(C) =8.90× 10⁻¹¹  F

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