Question

A 0.23-f capacitor is desired. What area must the plates have if they are to be separated by a 3.8-mm air gap?

Answer 1

The area of the plates must have is(A)= 9.91×10⁷ m²

How can we calculate the value of a area of a capacitor?

To calculate the the value of a area of the plates of a capacitor, we are using the formula,

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

Or, A= $\frac{C\times d}{\epsilon_0}$

Here we are given,

C= The desired capacitance of a capacitor.

= 0.23F

d=distance of separation between the plates.

=3.8mm= 0.0038m.

$\epsilon_0$= permittivity of the vacuum.  

=8.854×10⁻¹²F/m

We have to calculate the area of the plates must have = A m².

Now we put the known values in the above equation, we can get

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

Or, A=$\frac{0.23\times 0.0038}{8.854\times 10^{-12}}$

Or, A= 9.91×10⁷ m²

From the above calculation, we can conclude that the area of the plates must have is(A)= 9.91×10⁷m²

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