Capacitors: find the dielectric constant

In summary: The correct expression is:K= ((8.85E-12)(7.8E-6 F))/(1.5(1.3E-5)) = 0.0378In summary, the dielectric constant of the dielectric in a parallel plate capacitor with a capacitance of 7.8 μF, an area of 1.5 m^2, and a separation of 1.3 x 10-5 m is 0.0378.
  • #1
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Homework Statement


A parallel plate capacitor has a capacitance of 7.8 μF when filled with a dielectric. The area of each plate is 1.5 m^2 and the separation between the plates is 1.3 x 10-5 m. What is the dielectric constant of the dielectric?

Homework Equations


C= (K(8.85E-12)A)/d

The Attempt at a Solution


K= (1.5(7.8E-6 F))/((8.85E-12)(1.3E-5)
=1.02E11
 
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  • #2
Alice7979 said:

Homework Statement


A parallel plate capacitor has a capacitance of 7.8 μF when filled with a dielectric. The area of each plate is 1.5 m^2 and the separation between the plates is 1.3 x 10-5 m. What is the dielectric constant of the dielectric?

Homework Equations


C= (K(8.85E-12)A)/d

The Attempt at a Solution


K= (1.5(7.8E-6 F))/((8.85E-12)(1.3E-5)
=1.02E11
Your last expression is unclear because the parentheses do not work (I am assuming you forgot a closing parenthesis at the very end). Double check your algebra, it looks like you end up multiplying the capacitance by the area in finding K, which cannot be right.
 
  • #3
Alice7979 said:

Homework Statement


A parallel plate capacitor has a capacitance of 7.8 μF when filled with a dielectric. The area of each plate is 1.5 m^2 and the separation between the plates is 1.3 x 10-5 m. What is the dielectric constant of the dielectric?

Homework Equations


C= (K(8.85E-12)A)/d

The Attempt at a Solution


K= (1.5(7.8E-6 F))/((8.85E-12)(1.3E-5)
=1.02E11
I had the area and length switched, thank you
 

1. What is the purpose of finding the dielectric constant of a capacitor?

The dielectric constant of a capacitor is a measure of its ability to store electric charge. By finding this value, we can determine the overall capacitance of the capacitor and its efficiency in storing and releasing electrical energy.

2. How is the dielectric constant of a capacitor calculated?

The dielectric constant of a capacitor can be calculated by dividing the capacitance of the capacitor with a dielectric material by the capacitance of the same capacitor without the dielectric material. This ratio is also known as the relative permittivity of the dielectric material.

3. What factors can affect the dielectric constant of a capacitor?

The dielectric constant of a capacitor can be affected by the type of dielectric material used, its thickness, and its temperature. In general, materials with higher dielectric constants have higher capacitance values and are better insulators.

4. How does the dielectric constant impact the performance of a capacitor?

The higher the dielectric constant of a capacitor, the more electric charge it can store and the more efficient it will be in its function. A higher dielectric constant also allows for a smaller physical size of the capacitor, making it ideal for use in smaller electronic devices.

5. Can the dielectric constant of a capacitor change over time?

Yes, the dielectric constant of a capacitor can change over time due to factors such as aging, temperature changes, and exposure to moisture or other contaminants. This can affect the performance of the capacitor and may require replacement or recalibration in certain applications.

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