Capacitors & Dielectrics

In summary, the conversation discusses two identical capacitors, one empty and one filled with a dielectric, connected to a 11.0-V battery. The question asks for the potential difference across the plates of the filled capacitor that would result in the same amount of electrical energy stored as the empty capacitor. The conversation mentions relevant equations for charge, capacitance, and energy, and ultimately suggests equating the energy and substituting for the capacitance values to solve for the potential difference.
  • #1
kgigs6
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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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  • #2
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...
 
  • Like
Likes gracy
  • #3
got it! Thanks a lot!
 

What is a capacitor?

A capacitor is an electronic component that is designed to store and release electrical energy. It consists of two conducting plates separated by an insulating material, called a dielectric.

How do capacitors work?

When a voltage is applied to a capacitor, it causes one plate to accumulate a positive charge and the other plate to accumulate a negative charge. This creates an electric field between the plates, and the dielectric material prevents the charges from flowing between the plates. The capacitor stores the electrical energy in this electric field.

What is the purpose of a dielectric in a capacitor?

The dielectric material in a capacitor serves to increase the capacitance, or the ability to store electrical charge. It also serves to prevent the plates from coming into direct contact with each other, which could cause a short circuit.

What are some common types of dielectric materials used in capacitors?

Some common dielectric materials used in capacitors include ceramic, paper, mica, and plastic. The type of dielectric used depends on the specific application and desired characteristics of the capacitor.

How are capacitors used in electronic circuits?

Capacitors are used in electronic circuits for a variety of purposes, such as smoothing out power supplies, filtering signals, and storing energy for short bursts. They are also commonly used in timing circuits, oscillators, and filters.

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