Relationship Between Conductance and the Dielectric Constant

In summary: If so you can plot impedance vs frequency and fit to a model to get capacitance.In summary, the poster is new to the forum and is conducting an experiment on how the dielectric constant of a binary mixture changes with concentration and temperature using a parallel plate capacitor. However, they are facing an issue with their multimeter not measuring capacitance. Their advisor suggested finding the conductance to calculate the dielectric constant, but the poster is unsure how to relate the two. They have equations for capacitance and conductivity, but are still left with two unknowns. They are seeking help in finding a solution, possibly using AC source frequency to plot impedance and fit to a model to get capacitance.
  • #1
AnnaLinnea
1
0
Hello all,
I'm new to the forum so I hope I'm posting this in the correct section.
I'm currently conducting an experiment in which I'm examining how the dielectric constant of a binary mixture changes with concentration and temperature using a parallel plate capacitor for measurements. The only problem, however is that the multimeter I'm using doesn't measure capacitance. Here's what I can measure:
• DC volts
• AC volts
• DC current
• AC current
• Resistance
• Temperature
• Frequency

My advisor for this project initially suggested that I find the conductance (or conductivity?) in order to calculate the dielectric constant, however I've searched and searched but I can't seem to find a way to relate the two.
Here's what I got so far.
I know that conductivity can be used to calculate the imaginary part of the dielectric constant
[tex]\kappa=\epsilon'+j\epsilon''[/tex]
[tex]\kappa=\epsilon'+j\sigma/\omega[/tex]
where [itex]\kappa[/itex] is the dielectric constant, [itex]\sigma[/itex] is the conductivity and [itex]\omega[/itex] is the frequency.
but I'm not sure how I would find the real part [itex]\epsilon'[/itex]in order to get [itex]\kappa[/itex]
I've also got the equations
[tex]C=Q/V[/tex]
[tex]C=\kappa\epsilon_{0}\frac{A}{d}[/tex] where [itex]\epsilon_{0}[/itex] is the vacuum permittivity, [itex]A[/itex] is the area of the plate and [itex]d[/itex] is the distance between the plates.
Then for conductivity,
[tex]J=\sigma E[/tex]
[tex]G=\sigma\frac{A}{d}[/tex]
where [itex]J[/itex] is the current density and [itex]G[/itex] is the conductance
and so relating the two
[tex]C=\kappa\epsilon_{0}\frac{G}{\sigma}[/tex]
but that still leaves me with two unknowns, [itex]C[/itex] and [itex]\kappa[/itex]
I feel like there's a really simple, really obvious solution that I'm just not seeing...
Can anybody help me out?
 
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  • #2
Welcome

Given AC volts and AC current, you can get impedance. From that you can get capacitance.

Is you AC source variable in frequency?
 

1. What is conductance and how is it related to the dielectric constant?

Conductance is the measure of a material's ability to conduct electricity. It is the inverse of resistance and is measured in siemens (S). The dielectric constant, also known as the relative permittivity, is a measure of a material's ability to store electrical energy in an electric field. The relationship between conductance and the dielectric constant is that as the dielectric constant increases, the conductance decreases. This is because a higher dielectric constant means the material is better at storing electrical energy and therefore has a lower ability to conduct electricity.

2. How does the dielectric constant affect the conductance of a material?

The dielectric constant affects the conductance of a material by determining how much electrical energy can be stored in the material. As the dielectric constant increases, more electrical energy is stored in the material, making it less conductive. This is because the stored energy creates a barrier for the flow of electricity, resulting in a decrease in conductance.

3. How is the dielectric constant measured?

The dielectric constant is measured by comparing the capacitance of a material with that of a vacuum. The capacitance is a measure of the ability of a material to store electrical energy, and a vacuum is used as a reference point because it has a dielectric constant of 1. The ratio of the capacitance of the material to the capacitance of a vacuum gives the dielectric constant of the material.

4. What is the relationship between dielectric constant and permittivity?

The dielectric constant and permittivity are closely related concepts. The dielectric constant is the ratio of the permittivity of a material to the permittivity of a vacuum. Permittivity is a measure of a material's ability to store electrical energy in an electric field, while the dielectric constant is a measure of a material's ability to store electrical energy compared to a vacuum. In other words, the permittivity is a physical property of a material, while the dielectric constant is a relative measure.

5. How does temperature affect the relationship between conductance and the dielectric constant?

Temperature can affect the relationship between conductance and the dielectric constant in two ways. First, it can affect the dielectric constant of a material, as some materials have a temperature-dependent dielectric constant. Second, temperature can also impact the conductivity of a material, which can indirectly affect the relationship between conductance and the dielectric constant. This is because temperature can alter the movement of charged particles in a material, which can affect its ability to conduct electricity.

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