Interactive Impedance Simulation

This is an interactive simulation aimed at describing electrical impedance through an analogy with water and pipes.

Introduction

Impedance is the alternating-current (AC) equivalent of resistance for DC circuits (remember Ohms' law, $V=IR$). Impedance, $Z$ itself is a complex quantity, having both magnitude ($|Z|$) and phase-shift ($\Phi$). For an input potential, the output current will depend on both of these factors. Mathematically, we represent impedance as a complex number.

Impedance spectroscopy is frequently used to characterise the electronic and/or ionic conductivity of materials. In many cases, the behaviour can be modelled as a combination of ideal resistors and capacitors, which have different impedance behaviour:

• Resistor:
  • $|Z| = R$
  • $\Phi = 0$
• Capacitor
  • $|Z| = \frac{1}{\omega C}$
  • $\Phi = 90^{\circ}$ where $\omega$ is the angular frequency, $\omega = 2\pi f$.