Impedance sinusoidal electric fields

In impedance spectroscopy [IS also referred to as dielectric spectroscopy (DS)], a sinusoidal electric field is applied across a sample, and the resulting polarization (or electric displacement) is determined as a function of frequency. The frequency sweep typically ranges from about 1 MHz down to about 1 mHz, but measurement may be performed at higher frequencies by using special equipment. 

The complex permittivity is given by s (o)= C (o) /Co, analogous to equation (1) for the static case, where Co= A.Bold is the vacuum capacitance of a parallel-plate capacitor ( =area of the plate, So the vacuum permittivity and d the plate separation (A/d) must have dimensions in cm) and C is the complex capacitance of the same capacitor filled with the material under study. Under the influence of a sinusoidal electric field, the complex permittivity relates to the impedance through ... 

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