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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.

# Energy Stored in Capacitor

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

If two capacitors with respective capacitances $$1.0\,\mu\text{F}$$ and $$4.0\,\mu\text{F}$$ are connected in parallel across a $$300\text{ V}$$ potential difference, how much total energy is stored in the two capacitors?

What capacitance is required to store an energy of $$8\text{ kW}\cdot\text{h}$$ at a potential difference of $$1000\text{ V}?$$

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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