# Mutual inductance of two loops

I got to measure inductance of circuit with two loops connected like this:

simulate this circuit – Schematic created using CircuitLab

simulate this circuit

The box measures $L$. I have this formula $$M=\frac{L_1-L_2}{4}$$ and when I compute $M$, it's negative. Is that ok? What does it mean? Should I make the result absolute?

In one measurement, I got $L_1=-1394~ \mu H$ and $L_2=-1392~ \mu H$. That seems wierd. I measured like 10m long cables. Isn't that suspicious? What could make the result wrong like this?

Additional information:

I was measuring with frequency $200 kHz$ and cables are flat. PNLY and Twist. One loop was made by connecting two nearest wires in the cable.

• Where is the formula from? And yes, it looks suspicuous. At which frequency did you measure it? Do the inductors have cores? – venny Sep 28 '14 at 2:19
• frequency 200 kHz. I was measuring inductance of cables. Like PNLY and Twist flat cable. Inductors in the schema are there as symbols for inductance of loops made by wires od the cable. – user50222 Sep 28 '14 at 10:39
• The formula is taken from relations of inductance of two coils in serie and "antiserie" as in the schemas. $L = L_1 + L_2 - 2M$ and so. – user50222 Sep 28 '14 at 10:41

## 1 Answer

A negative value of inductance tells me the net impedance you measured is capacitive. If you are measuring cable inductance try measuring end to end rather than across one end. This answer presumes it is a multicore or coax cable you are trying to measure.

If your measurement system uses 1 kHz to determine impedance, an apparent inductance of 1.39 H would be an impedance of 8734 ohms and an 18.2 nF capacitor would produce the same "value" but phase shifted by 180 degrees hence giving you a minus sign for inductance - try switching the measurement equipment to "capacitance" to confirm this.

10m of cable would therefore have a capacitance of 1820 pF per metre. This sounds a little high so maybe the test frequency used by your measurement equipment is more like 3 kHz.