What is the energy stored in the capacitor?

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SUMMARY

The energy stored in a capacitor can be calculated using the formula \( E = \frac{1}{2} C V^2 \). In this discussion, a 15 µF capacitor is charged to 20 volts, resulting in an energy storage of 3 J. The initial confusion regarding 20 J was clarified, as the correct interpretation involves voltage rather than energy directly applied. The integration method discussed involves the relationship between voltage and charge, confirming that energy is stored as the capacitor charges up to 20 V.

PREREQUISITES
  • Understanding of capacitor fundamentals, including capacitance and voltage.
  • Familiarity with the formula for energy stored in capacitors: \( E = \frac{1}{2} C V^2 \).
  • Basic knowledge of calculus, specifically integration techniques.
  • Concept of electric potential and charge relationship in capacitors.
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  • Study the derivation of the energy stored in capacitors using calculus.
  • Learn about different types of capacitors and their applications in circuits.
  • Explore the impact of resistance on capacitor charging and energy loss.
  • Investigate advanced capacitor models, including dielectric materials and their effects on capacitance.
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Students in electrical engineering, physics enthusiasts, and professionals involved in circuit design and analysis will benefit from this discussion.

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20 J is placed across a 15uF capacitor. What is the energy stored in the capacitor?

any ideas on how to do this?
 
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donjt81 said:
20 J is placed across a 15uF capacitor. What is the energy stored in the capacitor?

any ideas on how to do this?
Check the question. I think it should be 20 volts not 20 J. (If 20 J is added to the capacitor, the energy stored in the capacitor is 20 J. because there is no energy is lost due to resistance).

The energy is [itex]\int_0^q Vdq[/itex] where V = potential (energy/charge) between the plates of the capacitor. It is 0 Volts initially but increases to 20 V. when fully charged.

Use the relationship between V and Q in a capacitor to express dq in terms of dV and then integrate with respect to V over the range 0 to 20 V.

AM
 

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