Dear Shakila Nur

I hope this message finds you well! I wanted to take a moment to address your great questions regarding Cole-Cole and Nyquist plots, which are indeed fundamental techniques in impedance spectroscopy. Let’s break them down to clarify their applications and calculations.

1. Total Capacitance in a Cole-Cole Plot

In a Cole-Cole plot, which represents a complex impedance plot (Z'' vs Z'), the total capacitance, denoted as C_total, can be derived from the shape of the plot. Ideally, you should observe a semicircle arc that corresponds to a single RC (resistor-capacitor) circuit. To calculate C_total, you can use the peak frequency f_peak of the semicircle with the following formula:

Ctotal​=1/(2πRfpeak)​

Here, (R) represents the resistance associated with the real part (Z') at the semicircle's intercept on the Z' axis.

2. Nyquist Plot: Considering Electrode Capacitance and Warburg Impedance

When interpreting a Nyquist plot, it’s essential to consider both the electrode capacitance and the Warburg impedance, especially if they are present. The Warburg impedance typically manifests as a linear tail at lower frequencies due to diffusion effects. If both the electrode capacitance and Warburg impedance are in parallel with a resistor (as seen in a Randles circuit), you Shakila Nur can apply the parallel formula:

1/Zparallel​=1/ZWarburg​​+1/Zcapacitance​1+1/R​

This method will help you Shakila Nur accurately interpret the Nyquist plot and gain insights into the behavior of the electrochemical system.

Thankful Prof @Kaushik Shandilya for helpful answer. Really appreciated. May I know if normally equivalent circuit with Warburg fitting will have high value capacitance?

Dear Dr, Kaushik Shandilya , is this equation can be used for cell or ceramic dielectric ? thank you Dr.