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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.

Gauss' Law for Capacitance

The concentric plates of a spherical capacitor have radii $$a=4.1\text{ mm}$$ and $$b=4.6\text{ mm}.$$ The above diagram shows the cross sectional feature of the capacitor. What is the approximate capacitance of the capacitor?

The value of the permittivity constant is $$\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.$$

What is the approximate capacitance of a copper sphere with a radius of $$2.50\text{ mm}?$$

The value of the permittivity constant is $$\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.$$

A cylindrical capacitor has radii $$a=1.1\text{ mm}$$ and $$b=2.9\text{ mm}$$ and length $$L=6.0\text{ cm},$$ as shown in the above cross sectional feature of the capacitor. What is the approximate capacitance of the capacitor?

The value of the permittivity constant is $$\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.$$

Suppose that $$4$$ identical mercury spheres with radius $$R=1.20\text{ mm}$$ are merged to one sphere. What is the approximate capacitance of the merged mercury drop?

The value of the permittivity constant is $$\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.$$

A parallel-plate capacitor has $$58.0\text{ cm}^2$$ of plate area and $$1.20\text{ mm}$$ separation. What is the approximate capacitance of the capacitor?

The value of the permittivity constant is $$\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.$$

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