Capacitors and Dielectrics of a circuit

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SUMMARY

The discussion centers on calculating the potential difference across a capacitor filled with a dielectric (k=5.00) to match the energy stored in an empty capacitor connected to a 6.0 V battery. The energy formula used is E=0.5CV², leading to the conclusion that the potential difference required for the dielectric-filled capacitor is 2.7 V. This is derived from the equation 6² = 5V², confirming that the energy stored in both capacitors is equal when the dielectric is considered.

PREREQUISITES
  • Understanding of capacitor energy storage equations (E=0.5CV²)
  • Knowledge of dielectric constants and their impact on capacitance
  • Familiarity with parallel plate capacitor equations (C=εA/d)
  • Basic algebra for solving equations involving variables
NEXT STEPS
  • Study the effects of different dielectric materials on capacitance and energy storage
  • Learn about the relationship between electric field strength and potential difference in capacitors
  • Explore advanced capacitor configurations and their applications in circuits
  • Investigate the role of dielectric breakdown and its implications in circuit design
USEFUL FOR

Electrical engineers, physics students, and anyone involved in circuit design or analysis, particularly those focusing on capacitors and dielectrics.

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Two capacitors are identical, except that one is empty and the other is filled with a dielectric ( k= 5.00). The empty capacitor is connected to a 6.0 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?

So here are my thoughts so far...
V= 6 V
Energy=.5CV^2
So the energy of the empty capacitor is .5V^2 which is .5(18^2)=18 right? they give no value for C so i assume it is one?
I have no idea where k comes into the picture. please help. thanks.
 
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What is the equation for the capacitance of a parallel plate capacitor in terms of epsilon, A (area) and d (separation distance), ignoring fringe effects at the edges? What is the relationship between epsilon-zero (vacuum value) and the epsilon inside the dielectric?
 
Answer

I just figured it out.
Energy=.5CV^2
Energy=.5kV^2

so .5CV^2=.5kV^2
so CV^2=kV^2
C=1
so V^2=kV^2
so 6^2=5V^2
so V= sqrt(36/5)=2.7 V
 

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