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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 parallel-plate capacitor with a plate area of \(1.90\text{ cm}^2\) and the separation between two plates of \(3.00\text{ mm}.\) It is charged fully by a \(8.00\text{ V}\) battery and then disconnected from the battery. Then approximately how much work is required to pull apart the plates to a separation of \(7.00\text{ mm}?\)

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

If a parallel-plate capacitor with plate area \(40\text{ cm}^2\) and plate spacing \(1.2\text{ mm}\) is charged to a potential difference of \(500\text{ V},\) how much energy is stored in the capacitor?

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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