Effects of Distance and Voltage on Energy Stored in Capacitors

In summary, as the distance between two parallel plates is increased while they remain hooked to a battery, the energy stored in the capacitor will decrease due to the decrease in capacitance. Similarly, if the distance is doubled and the battery voltage is also doubled, the energy stored in the capacitor will increase by a factor of 2 according to the equations Q = VC and U2 = (Q2)/(2C) = 1/2C(V2). Additionally, the equation for capacitance, C = (εr·A)/(4πd), can be substituted into the energy equation to draw further conclusions.
  • #1
displayname
6
0

Homework Statement



The distance between two parallel plates is increased while
they remain hooked to a battery. The energy stored in the
capacitor will:

AND

The distance between two parallel plates is doubled while
they remain hooked to a battery. The battery voltage also is
doubled. The energy stored in the capacitor will:

Homework Equations



Q = VC
U2 = (Q2)/(2C) = 1/2C(V2)

The Attempt at a Solution



As the distance is increased, the capacitance will decrease. Since energy is directly related to capacitance, the energy will also decrease? I'm not sure if I'm right.
 
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  • #2
displayname said:
As the distance is increased, the capacitance will decrease. Since energy is directly related to capacitance, the energy will also decrease? I'm not sure if I'm right.

You are right. Even more right, the energy in a capacitor is (1/2)CV2, or (1/2)Q2/C. Make with that what you will!
 
  • #3
so for the second question, energy increases by a factor of 2. Right?
 
  • #4
If that's what the equations say, then that's what it is!
 
  • #5
Another equation you will need is for capacitance.

690d608cf871d5c6e822647d0a0cb583.png


where
C is the capacitance;
A is the area of overlap of the two plates;
εr is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates (for a vacuum, εr = 1);
and d is the separation between the plates.

So substitute C with the physical equation into the energy equation

U2 = (Q2)/(2C) = 1/2C(V2)

U2 = 1/2·(εr·A/(4πd))·(V2)

You can draw your own conclusions from here.

Info from Wikipedia -> http://en.wikipedia.org/wiki/Capacitance" [Broken]
 
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1. What is the difference between a capacitor and a battery?

A capacitor is an electronic component that stores energy in an electric field. It can release energy quickly, but can only hold a small amount of charge. A battery, on the other hand, is a chemical device that converts chemical energy into electrical energy. It can hold a larger amount of charge for a longer period of time.

2. How do capacitors and batteries work together in electronic devices?

Capacitors and batteries often work together in electronic devices to regulate and store electrical energy. Batteries provide a steady source of power, while capacitors can help smooth out any fluctuations in the electrical current. Capacitors can also be used to store energy from the battery, allowing it to discharge quickly when needed.

3. What are the different types of capacitors and batteries?

There are various types of capacitors, including electrolytic, ceramic, and film capacitors. Each type has different properties and is used for different purposes. Batteries also come in different types, such as lead-acid, lithium-ion, and nickel-metal hydride. Each type has its own advantages and disadvantages, making them suitable for different applications.

4. How do you calculate the energy storage capacity of a capacitor or battery?

The energy storage capacity of a capacitor is calculated by multiplying the square of its voltage by its capacitance. For batteries, the energy storage capacity is determined by multiplying the battery's voltage by its amp-hour rating. It is important to note that the actual storage capacity may vary depending on the specific conditions and usage of the capacitor or battery.

5. How should I properly dispose of capacitors and batteries?

Capacitors and batteries should be disposed of properly to avoid any harm to the environment. Most municipalities have designated electronic waste recycling centers where you can drop off these items. It is important to follow local guidelines and regulations for the safe disposal of these electronics.

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