Physics homework problem - design a capacitor

In summary, the conversation discusses designing a capacitor with a capacitance of 1*10-6F using a material with a dielectric constant of 260 and a maximum voltage allowance of 160 volts. The engineer must determine the area of the plates, which can be done using the equation A=4πkdC. However, the dielectric constant and dielectric strength values must be taken into account. The maximum voltage is important because it determines the dielectric strength and ultimately the distance between the plates.
  • #1
mondroid
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Physics homework problem -- design a capacitor

Homework Statement


An engineer needs to design a capacitor with a capacitance of 1*10-6F using a material with a dielectric constant 260. If the dielectric strength of the material is 8*106 N/C, and the maximum voltage that the capacitor is allowed to handle is 160 volts, what must be the area of the plates?

Homework Equations


Q=CV, C=A/(4πkd)


The Attempt at a Solution



A=4πkdC; everything is known except the distance between plates

V=Ed, d=V/E; V is given

E=kq/r2, r=d

d=kq/V

A=4πk2CQ/V

I got A = .113m2 but I'm not sure If I'm doing it right or not. Could some check it for me please. I did not use the dielectric constant and dielectric strength values.

Thank you
 
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  • #2
I did not use the dielectric constant and dielectric strength values.
Then you are doing it wrong.

What is important about the maximum voltage?
It is the voltage, above which, the capacitor does something special...
 
  • #3
Dielectric strength can also be written as[itex]\frac{V}{m}[/itex], and Max Voltage on a capacitor is dielectric strength * distance between the plates.

Hope this helps.
 

1. What is a capacitor and how does it work?

A capacitor is an electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied to the capacitor, one plate becomes positively charged and the other becomes negatively charged, creating an electric field between them. This electric field stores the energy until it is discharged.

2. How do you design a capacitor for a specific application?

The design of a capacitor involves determining the capacitance, or the ability to store charge, required for the specific application. This can be calculated using the formula C = εA/d, where C is the capacitance, ε is the permittivity of the dielectric material, A is the area of the plates, and d is the distance between the plates. The type of dielectric material and the distance between the plates can be chosen based on the desired capacitance and other factors such as size and cost.

3. What factors affect the capacitance of a capacitor?

The capacitance of a capacitor is affected by several factors, including the area of the plates, the distance between the plates, and the type of dielectric material used. Increasing the area of the plates or decreasing the distance between them will increase the capacitance. Different dielectric materials have different permittivity values, which also affects the capacitance. Additionally, the shape and placement of the plates can also impact the capacitance.

4. How do you calculate the energy stored in a capacitor?

The energy stored in a capacitor can be calculated using the formula E = 1/2CV^2, where E is the energy, C is the capacitance, and V is the voltage applied to the capacitor. This formula shows that the energy stored in a capacitor is directly proportional to both the capacitance and the square of the voltage applied to it.

5. What are some common applications of capacitors?

Capacitors have a wide range of applications in electronic circuits, including energy storage, filtering, and timing. They are commonly used in power supplies, audio systems, and electronic devices such as cameras and computers. They are also used in electric motors, flashlights, and other devices that require a temporary surge of power.

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