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# Capacitors and Transformers

Capacitors are devices that accumulate voltage in separated electric charges, but their mechanism and mathematics can describe thermal insulation and the discharge of lightning from cloud to ground.

Consider a spherical capacitor which consists of two concentric spherical shells of radii \(38.0\text{ mm}\) and \(40.0\text{ mm},\) respectively. If we want to make a parallel-plate capacitor with the same separation, what must be the area of each plate for the same capacitance?

The value of electrostatic constant is \(\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2\) and the value of the permittivity constant is \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)

If the radius of the smaller ball is \(5~\mbox{cm}\) and of the bigger sphere \( 15~\mbox{cm}\), which capacitance **in pF** do you expect to obtain?

**Details and assumptions**

- The ball and the sphere are centered around the same point

If you want to make a parallel-plate capacitor of capacitance \(0.9\text{ pF}\) with two metal plates with area \(1.1\text{ cm}^2,\) what must be the separation between the two plates?

The value of the permittivity constant is \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)

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