Solving Solid State Problem: Find ε'(ω) & ε''(ω)

In summary, the conversation is about solving a circuit with two branches, one containing a capacitor and the other containing a series of capacitor and resistor. The goal is to show that this circuit is equivalent to a capacitor with a dielectric satisfying the Dybe equation. The person has found the total impedance but is struggling to extract the real and imaginary parts and apply the Debye relation. They ask for ideas and for the person to show their progress so far.
  • #1
yoyaaaaaaa
2
0

Homework Statement





please can anyone answer this question

consider the parallel arrangement of the following two circuit branches , one branch consists of a capacitor C1 , the other of a capacitor C2 series with resistance R . show that this circuit is equivalent to a capacitor with a dielectric satisfying Dybe equation ( ε'(ω) and ε''(ω)). Find them

i got total impedence but i can't extract ε'(ω) and ε''(ω)

please share ur ideas
 
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  • #2
Please first show us what you've got so far. (read the Guidelines)
 
  • #3
i made Z(total)= 1/jωC2//(1/jωC2+R) then i got real part of Z +imaginary part of Z but it must be equivalent to a capacitor has real part and imaginary part

and up to this step i couldn't find ε'(ω) and ε''(ω)
 
  • #4
Can you write down what you get for Re(Z) and Im(Z) as well as the Debye relation?
 

1. What is the importance of finding ε'(ω) and ε''(ω) in solving solid state problems?

Finding the real (ε') and imaginary (ε'') parts of the dielectric function ε(ω) is essential in understanding the behavior of materials under applied electric fields. These values provide information about the material's ability to polarize and respond to an external electric field, which is crucial in many solid state applications.

2. What is the relationship between ε'(ω) and ε''(ω)?

The real and imaginary parts of the dielectric function are related through the Kramers-Kronig relations. This means that knowing one part allows us to calculate the other part, providing a complete picture of the material's dielectric response.

3. How is ε'(ω) and ε''(ω) measured experimentally?

The dielectric function can be measured using various techniques such as ellipsometry, infrared spectroscopy, and terahertz spectroscopy. These methods involve measuring the reflected or transmitted light from a material and using mathematical models to extract the dielectric function.

4. What factors can affect the values of ε'(ω) and ε''(ω)?

The dielectric function of a material can be influenced by several factors such as temperature, crystal structure, and the presence of impurities or defects. Changes in any of these factors can alter the dielectric response of a material.

5. How can the values of ε'(ω) and ε''(ω) be used in practical applications?

The dielectric function is used in the design and optimization of electronic and optoelectronic devices, such as solar cells, LEDs, and transistors. It is also crucial in understanding the behavior of materials in fields like solid state physics, materials science, and semiconductor technology.

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