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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 \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)

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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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In the above circuit, the potential difference across the capacitor arrangement is \(V=100\text{ V}\) and the capacitance are \[C_1=10.00\,\mu\text{F}, C_2=5.00\,\mu\text{F}, C_3=2.00\,\mu\text{F}.\] Approximately how much energies are stored for the capacitors \(1 (U_1\)) and \(2 (U_2\)), respectively?

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