Elements of Electrical Circuits

EIS data are commonly analyzed by fitting them to a model of an equivalent electrical circuit. Most of the circuit components in the model are common electrical elements such as resistors, capacitors, and inductors. To be useful, the elements in the model should have a basis in the physical electrochemistry of the system. As an example, most models contain a resistor that models the cell’s solution resistance.

Some knowledge of the impedance of the standard circuit components is therefore quite useful. The following table lists the common circuit elements, the relevant equation relating current to voltage, and their impedance.

Common Electrical Components

Component Relationship of Current and Voltage Impedance

Resistor

• E = IR
• Z = R

Inductor

• E = L di/dt
• Z = jωL

Capacitor

• I = C dE/dt
• Z = 1/(jωC)

Notice that the impedance of a resistor is independent of frequency and has only a real component. Because there is no imaginary impedance, the current through a resistor is always in phase with the voltage.

The impedance of an inductor increases as frequency increases. Inductors have only an imaginary impedance component. As a result, an inductor’s current is phase shifted 90° with respect to the voltage.

The impedance versus frequency behavior of a capacitor is opposite to that of an inductor. A capacitor’s impedance decreases as the frequency is raised. Capacitors also have only an imaginary impedance component. The current through a capacitor is phase shifted –90° with respect to the voltage.