How Does a Dielectric Affect Capacitor Voltage for Equal Energy Storage?

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SUMMARY

The discussion focuses on determining the potential difference across the plates of a capacitor filled with a dielectric (κ = 3.20) to ensure it stores the same electrical energy as an empty capacitor connected to an 11.0-V battery. The relevant equations include the capacitance formulas C = EoA/d and C = kEoA/d, along with the energy stored in a capacitor U = 1/2qV. By equating the energies of both capacitors (U1 = U2) and substituting the capacitance equations, the potential difference V2 can be expressed in terms of the known voltage V1.

PREREQUISITES
  • Understanding of capacitor fundamentals, including capacitance and energy storage.
  • Familiarity with dielectric materials and their effect on capacitance.
  • Knowledge of the equations governing capacitors, specifically U = 1/2qV and C = kEoA/d.
  • Basic algebra skills for manipulating equations and solving for unknowns.
NEXT STEPS
  • Study the impact of different dielectric constants on capacitor performance.
  • Learn how to derive energy equations for capacitors with varying configurations.
  • Explore practical applications of capacitors in electronic circuits.
  • Investigate the relationship between voltage, charge, and capacitance in more complex capacitor systems.
USEFUL FOR

Students in physics or electrical engineering, educators teaching capacitor theory, and anyone interested in the practical applications of capacitors in circuits.

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Homework Statement



Two capacitors are identical, except that one is empty and the other is filled with a dielectric (κ = 3.20). The empty capacitor is connected to a 11.0-V battery. What must be the potential difference across the plates of the capacitor filled with a dielectric such that it stores the same amount of electrical energy as the empty capacitor?

Homework Equations



q = cV
C = EoA/d
C = kEoA/d
U = 1/2qV
U = 1/2cV^2

The Attempt at a Solution



I'm not sure which form of the equation to use exactly. I know that since everything in the capacitors is equal except the dielectric I should be able to set them equal to each other some how and since I only know the voltage of the battery most of the terms will cancel out but I'm unsure of where to start. If someone could point me in the right direction that would be great!
 
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you know the equation for C1 & C2, only differ by k term

you want to fiond V2 in terms of V1

and you know
U1 = U2

so equate the energy, subtitute for the C's & solve in terms of for V2 in terms of V1...
 
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Likes   Reactions: gracy
got it! Thanks a lot!
 

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