Is a Spool of Hookup Wire an Inductor?

We started with 100 feet of 22 gauge wire…

First, a Measurement

Using an LCR meter we measure the wire’s inductance to be 731.8µH at 10kHz.The meter says it’s an inductor.

Let’s Test with a Circuit

We decided to measure phase shift with a simple series RL circuit measured at 10kHz.

A 45o shift should occur when XL = R.

Inductive reactance is computed by:XL = 2πfLXL = 6.28 x 10kHz x 731.8µHXL= 45.957Ω

We used a 46.6 Ω resistor in our circuit to match the XL at 10kHz.

Connections to Signal Generator and Scope

Output Compared to InputThe larger, yellow waveform is the source while the smaller is the signal across the resistor. There is phase shift!

According to Ө = tan-1 XL/R Ө = tan-1 45.957Ω / 46.6 ΩӨ = 44.6o

Measuring the Phase Shift This is a better look at the waveforms.

Start by equating scope divisions to degrees. Our source waveform shows each horizontal division is equivalent to 36o.

In an inductive circuit, the voltage across the resistor lags the source voltage. This is clear in the image.

180o /5 Div = 36o per division

Measuring the Phase Shift (continued)

Measuring the phase shift between the two waveforms involves interpreting the difference in spacing between similar points on each waveform.

The source crosses zero going negative 1.3 divisions before the resistor output waveform does the same.

Since each division is equal to 36o the phase shift for the circuit is 1.3 x 36o = 46.8o - Close to 45o

Difference between source and output is 1.3 divisions

What Happens if We Unspool the Wire?

What Happens if We Unspool the Wire?

Here is the circuit with the hookup wire fully unspooled. Not much to look at because the wire is draped all over the lab and the resulting circuit is just the resistor connected to the signal generator with 100 feet of wire.

We should expect the uncoiling of the wire to substantially affect the inductance properties and affect the phase shift.

What Happens if We Unspool the Wire?

This is the source voltage compare to the resistor voltage with the spool uncoiled.

The two signals are virtually in phase which is the outcome expected in a purely resistive circuit.

Coils of Wire Have Inductance!