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Electricity and Magnetism

Capacitors and Transformers

Concept Quizzes

Capacitors
Energy stored in a capacitor
Gauss' law to find capacitance

Challenge Quizzes

Capacitors and Transformers: Level 2-3 Challenges
Capacitors and Transformers: Level 3-4 Challenges

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

2.86 \times 10^{-9} \text{ J}

2.39 \times 10^{-11} \text{ J}

3.10 \times 10^{-8} \text{ J}

2.62 \times 10^{-10} \text{ J}

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by Brilliant Staff

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

14.8 \,\mu\text{J}

3.7 \,\mu\text{J}

7.4 \,\mu\text{J}

11.1 \,\mu\text{J}

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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?

0.18 \text{ J}

0.23 \text{ J}

0.45 \text{ J}

0.14 \text{ J}

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

57.6 \text{ F}

40.3 \text{ F}

69.1 \text{ F}

86.4 \text{ F}

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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?

U_1=5.54\times 10^{-3}\text{ J}, U_2=1.11\times 10^{-2}\text{ J}

U_1=3.33\times 10^{-3}\text{ J}, U_2=1.56\times 10^{-2}\text{ J}

U_1=3.33\times 10^{-3}\text{ J}, U_2=1.11\times 10^{-2}\text{ J}

U_1=5.54\times 10^{-3}\text{ J}, U_2=1.56\times 10^{-2}\text{ J}

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by Brilliant Staff