Measurement of mutual inductance from frequency dependence of impedance of AC coupled circuit using digital dual-phase lock-in amplifier

We present a simple method to determine the mutual inductance $M$ between two coils in a coupled AC circuit by using a digital dual-phase lock-in amplifier. The frequency dependence of the real and imaginary parts is measured as the coupling constant is changed. The mutual inductance $M$ decreases as the distance $d$ between the centers of coils is increased. We show that the coupling constant is proportional to $d^{-n}$ with an exponent $n$ ($\approx$ 3). This coupling is similar to that of two magnetic moments coupled through a dipole-dipole interaction.