Capacitors: find the dielectric constant

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SUMMARY

The discussion centers on calculating the dielectric constant (K) of a parallel plate capacitor with a capacitance of 7.8 μF, plate area of 1.5 m², and plate separation of 1.3 x 10-5 m. The formula used is C = (K * ε0 * A) / d, where ε0 is 8.85E-12 F/m. The initial calculation resulted in an incorrect value due to a mix-up in the area and length, leading to a dielectric constant of 1.02E11, which was identified as erroneous. Correcting the algebra is essential for accurate results.

PREREQUISITES
  • Understanding of parallel plate capacitor theory
  • Familiarity with the formula for capacitance C = (K * ε0 * A) / d
  • Knowledge of the physical constants, specifically ε0 (8.85E-12 F/m)
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Review the derivation of the capacitance formula for parallel plate capacitors
  • Practice calculating dielectric constants using different values of capacitance, area, and separation
  • Explore the effects of different dielectric materials on capacitance
  • Learn about the applications of capacitors in electronic circuits
USEFUL FOR

Students studying electrical engineering, physics enthusiasts, and anyone involved in capacitor design or analysis will benefit from this discussion.

Alice7979
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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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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.
 
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
 

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