Energy changes upon insertion of a solid dielectric in a capacitor

In summary, when charging a capacitor at a constant voltage, the voltage source can have the same voltage as the capacitor. This allows the difference in potential to be dissipated in the battery or in the wires, which results in a higher efficiency than charging at a variable voltage.
  • #1
GKRM
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Consider a simple circuit consisting of a battery and a parallel plate capacitor .During the process of charging of capacitors, we come to learn that half of the work done by the battery is stored in the form of potential energy and half of it is lost as heat or electromagnetic radiation.

Consider another arrangement consisting of parallel plate capacitor with its terminals connected with a battery to maintain a constant potential difference V₀ between it's terminals. Now I partially immerse a solid dielectric into this capacitor. The dielectric will feel an attractive force. Due to its further penetration inside the dielectric the potential energy of the system changes due to transfer of charge to maintain a constant potential difference . To calculate the force on the dielectric by this method , why do we neglect any loss of heat and say that all the work done by battery leads to change in potential energy of the system + the change in kinetic energy of the dielectric slab (with no energy loss as heat or electromagnetic radiation), while we can't neglect the loss in the aforementioned case. Can you please explain this?

Thanks in advance.
 
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  • #2
The difference is that when charging the capacitor with a constant voltage source, the potential across the capacitor varies, and is only half the voltage of the voltage source on average, so the difference must be dissipated in the battery or in the wires, while when adding charge to a capacior at constant voltage, the voltage source can have the same voltage as the capacitor.

BTW, You can beat the 50% efficiency when charging a capacitor if you use a buck/boost voltage regulator with a varying voltage.
 
  • #3
Thanks a lot for your reply. Well I'm a high school student and I don't have much knowledge regarding the devices you've mentioned. I'm highly constricted within my course syllabi. I would be happy if you throw some light on energy losses on insertion of dielectric at constant voltage ( a DC voltage)
 

1. How does inserting a solid dielectric affect the energy stored in a capacitor?

Inserting a solid dielectric in a capacitor increases the amount of energy that can be stored. This is because the dielectric material reduces the electric field between the plates of the capacitor, allowing for a higher charge to be stored on the plates without causing breakdown.

2. What is the relationship between the dielectric constant of a material and the energy stored in a capacitor?

The dielectric constant, also known as the relative permittivity, is a measure of a material's ability to store electric charge. The higher the dielectric constant, the more energy can be stored in a capacitor with that material as the dielectric.

3. Does the energy stored in a capacitor change if a dielectric is inserted between the plates?

Yes, the energy stored in a capacitor increases when a dielectric is inserted between the plates. This is because the dielectric reduces the electric field, allowing for a larger charge to be stored on the plates without causing breakdown.

4. Can any material be used as a dielectric in a capacitor?

No, not all materials can be used as dielectrics in a capacitor. A dielectric material must have a high dielectric constant and be able to withstand high voltages without breaking down. Materials commonly used as dielectrics include mica, ceramic, and plastic.

5. How does the thickness of a dielectric affect the energy stored in a capacitor?

The thickness of a dielectric does not affect the energy stored in a capacitor, as long as the dielectric material is able to withstand the electric field without breaking down. However, a thicker dielectric can lead to a larger capacitance, which in turn can increase the amount of energy that can be stored in the capacitor.

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