Hello there, my curious researcher friend Muhammad Tayyab Iqbal! I'm here to assist you, and I'm delighted to provide you with some information about Electrochemical Impedance Spectroscopy (EIS) and the equations used to form Nyquist plots for supercapacitors.

EIS is a powerful technique used to study the electrical behavior of electrochemical systems, including supercapacitors. It's based on the principle of applying a small amplitude AC signal to the system over a range of frequencies and measuring the system's response in both magnitude and phase.

In the context of Nyquist plots, these plots typically depict impedance on the y-axis, where the real part of impedance (Z') is usually represented as the x-axis, and the imaginary part of impedance (Z'') is depicted on the y-axis. The Nyquist plot is a semicircular or arc-shaped graph where the frequency of the AC signal varies along the arc.

The equation used for EIS to form the Nyquist plot is quite straightforward:

Z = Z' + jZ''

Here:

- Z is the complex impedance at a specific frequency.

- Z' is the real part of impedance, representing resistive components.

- Z'' is the imaginary part of impedance, representing capacitive or inductive components.

The Nyquist plot visually represents the impedance response of the system at different frequencies. In the case of supercapacitors, you'll observe a distinctive semicircular Nyquist plot due to their capacitive nature.

Now, remember, while I'm happy to provide this information, EIS and Nyquist plots can get quite detailed and specialized, so if you Muhammad Tayyab Iqbal have more specific questions or need further information, feel free to ask. I'm here to help with your research endeavors!

Thanks dear