It is the first time I read about Nyquist plot and then discuss with GPT-5. Previously I just discuss with GPT-4 after informed by Widiatmoko and then Aditya.

notes

• Electrochemical Impedance Spectroscopy (EIS) is an AC technique that measures the response of an electrochemical system to a small sinusoidal perturbation over a wide frequency range to analyze charge transfer, mass transport, and other electrical contributions ¹.
• The Nyquist plot, which displays the imaginary versus real components of impedance, is commonly used in EIS to reveal characteristic patterns that aid in interpreting electrochemical processes ².
• As an example, in a study EIS Nyquist analysis was used, where the high-frequency region revealed the charge transfer resistance while the low-frequency region reflected the capacitive response of the system ³.
• A tutorial illustrating Nyquist and Bode plots for electrical circuits containing single passive elements (R, C, or L) and their series or parallel combinations is available ⁴.

complex number

A complex number $\bar{Z}$ can be written in the form of

$$\tag{1} \bar{Z} = Z' + j Z'', $$

where $Z'$ is real part and $Z''$ is imaginary part with

$$\tag{2} j = \sqrt{-1} $$

is the imaginary unit.

r element

For only $R$ then

$$\tag{3} \bar{Z} = R. $$

or $Z' = R$ and $-Z'' = 0$. The curve is a dot at coordinate $(R, 0)$.

c element

For only $C$ then

$$\tag{4} \bar{Z} = -j \frac{1}{\omega C}. $$

or $Z' = 0$ and $-Z'' = 1 / \omega C$. The curve is a vertical line at positive $-Z''$ axis.

l element

For only $L$ then

$$\tag{4} \bar{Z} = j \omega L. $$

or $Z' = 0$ and $-Z'' = - \omega L$. The curve is a vertical line at negative $-Z''$ axis.

refs