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

AI Thread Summary
To determine the voltage across a capacitor filled with a dielectric that stores the same energy as an empty capacitor, it is essential to equate their energy formulas. The energy stored in a capacitor is given by U = 1/2CV^2, where C is the capacitance and V is the voltage. For the empty capacitor, the capacitance is C1 = EoA/d, while for the dielectric-filled capacitor, C2 = κEoA/d. By setting U1 equal to U2 and substituting the capacitance formulas, the relationship between the voltages can be derived, leading to V2 being expressed in terms of V1. This approach allows for solving the problem effectively.
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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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got it! Thanks a lot!
 

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