Parallel plate capacitors

In summary: The distance between the plates increases by 3.02 mm, which results in a capacitance of 4.311536113 x 10 ^-5 J.
  • #1
map7s
146
0

Homework Statement



A parallel-plate capacitor has plates with an area of 445 cm2 and an air-filled gap between the plates that is 1.51 mm thick. The capacitor is charged by a battery to 575 V and then is disconnected from the battery. There is 4.311536113 x 10 ^-5 J of energy stored in the capacitor. The separation between the plates is now increased to 3.02 mm. How much energy is stored in the capacitor now?

Homework Equations



I know that since the capacitor is disconnected from the battery, V can change with C while Q, being trapped in the disconnected
capacitor, is constant. I calculated Q for the original
capacitor, which was about 1.5 x 10^-7 C. When the spacing, d, between the plates is increased, C changes, and V changes with it, so I know that I can't use the equation U=(1/2)CV^2 (with V=575 V) to find the energy, but I'm not sure exactly what I can use.
 
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  • #2
map7s said:
...When the spacing, d, between the plates is increased, C changes, and V changes with it...

So let's see how they change.
 
  • #3
Well, I thought that maybe by treating the increased space as a dielectric field and using the dielectric constant I could figure out the new values of V and C and use the Q to calculate the new Energy, but apparently I wasn't on the right track...
 
  • #4
How is the capacitance related to the distance between the plates?
 
  • #5
In calculating the capitance, the equation is C=(constant) x area/distance. So, b/c the battery is disconnected and the plates are pulled further away from each other, there needs to be a new equation for capitance...but I'm not sure what
 
  • #6
map7s said:
...there needs to be a new equation for capitance...but I'm not sure what

Not a new equation. Only a new value for one parameter - the distance between the plates.

By how many times does the distance between the plates increase? How will this affect the capacitance? Will it become greater or smaller? By how many times?
 

1. What is a parallel plate capacitor?

A parallel plate capacitor is a type of electronic component that is used to store electric charge. It consists of two parallel conductive plates separated by an insulating material, also known as a dielectric. When a voltage is applied to the capacitor, it stores electric charge on its plates, creating an electric field between them.

2. How does a parallel plate capacitor work?

A parallel plate capacitor works by storing electric charge on its plates. The plates are connected to a source of voltage, and when the voltage is applied, one plate becomes positively charged while the other becomes negatively charged. This creates an electric field between the plates, which allows the capacitor to store charge.

3. What factors affect the capacitance of a parallel plate capacitor?

The capacitance of a parallel plate capacitor is affected by several factors, including the distance between the plates, the surface area of the plates, and the type of dielectric material used. Generally, a larger distance between the plates and a larger surface area will result in a higher capacitance, while a higher dielectric constant of the material will also increase the capacitance.

4. What are the applications of parallel plate capacitors?

Parallel plate capacitors have a variety of applications, including in electronic circuits for filtering, tuning, and energy storage. They are also commonly used in power supplies, electric motors, and radio frequency amplifiers. Capacitors are also essential components in many electronic devices, such as computers, smartphones, and televisions.

5. What are the advantages of using parallel plate capacitors?

Parallel plate capacitors have several advantages, including their ability to store large amounts of energy in a relatively small space, their low cost, and their ability to work in a wide range of temperatures. They also have a high tolerance for voltage and are able to withstand high voltages without breaking down. Additionally, capacitors have a long lifespan and can be easily replaced if needed.

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