Calculating Voltage and Capacitance Given Stored Energy in a Capacitor

Introduction to Capacitors and Energy Storage

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Care has been taken to thoroughly address a question involving the calculation of voltage and capacitance given the stored energy in a capacitor. This article ensures that the provided values are realistically applicable and explains the underlying physics behind the calculation. Let's delve into the details.

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Understanding the Given Values

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A capacitor is charged with a charge of 10,000 microcoulombs (10,000 x 10-6 coulombs), and the energy stored in it is 1 joule. The logical steps to determine the voltage and capacitance are outlined here.

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Step-by-Step Calculation

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Given:

r r Charge (Q) 10,000 x 10-6 coulombsr Energy stored (E) 1 jouler r r

The formula for energy stored in a capacitor is:

r

E 0.5 * C * V2r

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Deriving the Voltage (V)

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We also know that:

r

E Q * V

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Substituting the given values:

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1 10,000 x 10-6 * V

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Solving for V:

r

V 1 / (10,000 * 10-6) 1 / 0.01 100 volts

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Deriving the Capacitance (C)

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Now, using the energy stored equation:

r

1 0.5 * C * V2

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Substituting the value of V:

r

1 0.5 * C * (100)2r

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1 0.5 * C * 10,000

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1 5,000 * C

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Solving for C:

r

C 1 / 5,000 2 x 10-4 farads 200 microfarads

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Verification and Real-World Application

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Thus, a capacitor charged with 10,000 microcoulombs, which is storing 1 joule of energy, has a voltage of 100 volts and a capacitance of 200 microfarads.

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Importance and Relevance to Real-World Applications:

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Understanding the calculation of voltage and capacitance given stored energy is essential in the design and analysis of electrical circuits, from basic electronics to advanced power systems. It allows engineers and technologists to optimize circuit performance and ensure safety and efficiency.

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Conclusion:

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The values provided in this calculation are not arbitrary but are rooted in fundamental physical principles. They are used in real-world applications, from power supplies and filters to energy storage systems, making them highly relevant in engineering and technology.

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Frequently Asked Questions (FAQs)

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Q: Why is the concept of capacitance important?

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A: Capacitance is crucial for energy storage, filtering, and smoothing out voltage levels in electrical systems. It plays a vital role in many electronic devices, from small circuits to large power systems.

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Q: How can I apply this knowledge practically?

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A: Knowledge of capacitance and energy storage is applied in designing power supplies, filtering noisy signals, and storing energy in renewable energy systems like capacitive energy storage. Understanding these principles allows for efficient and effective design solutions.

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Final Thoughts

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While the given values may seem trivial in a theoretical context, they embody the principles that govern real-world applications. Always seek to understand the fundamental concepts to apply them effectively in various scenarios.