Capacitors and Dielectrics of a circuit

AI Thread Summary
Two identical capacitors are compared, one empty and one filled with a dielectric (k=5.00), connected to a 6.0 V battery. The energy stored in the empty capacitor is calculated using the formula Energy = 0.5CV^2, leading to a value of 18 when assuming C=1. The relationship between the two capacitors is established by equating their energy storage, resulting in the equation CV^2 = kV^2. Solving this gives the potential difference across the dielectric-filled capacitor as approximately 2.7 V. Thus, the filled capacitor must have a potential difference of 2.7 V to store the same energy as the empty one.
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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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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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