Why did disconnecting an electrical coil create a jolt in my arm?

Question

Way (way) back in the day, I was doing a physics experiment (LC circuit behavior, IIRC, but that’s not important) part of which involved a large-ish (maybe 12” diameter, 2” thick) desktop coil in a circuit connected to a 12v (DC, I think) supply. At various points, I had to disassemble part of the setup, and then bolt it back together in a different way. For each such disassemble/reassemble portion, the instructions stressed that we should first “always turn off the power supply”.

I merrily got on with the experiment, and everything was going fine and as expected until at one point I forget the “always turn off the power supply” part. I noticed two things:

1. When I tried to pull one of the banana-clip terminated cables running into the coil, it seemed much stiffer and harder to extract than previously (i.e. when I had remembered to power-down first); AND

2. When I finally got it out, after hauling quite hard, I felt a jolt in my elbow, and my arm actually twitched slightly at that joint. It wasn’t painful, but it was not small. If I remember (again, it was way back) it felt something akin to the way your knee reacts when a doctor hits your patellar tendon with a reflex hammer.

Since then, I’ve always remembered it as being an example of Back EMF. But I just had reason to refresh my memory of that concept and I’m now not so sure that’s the explanation at all; or at least, not the entire explanation.

So what exactly did I experience? What is the name(s) for the resistance I felt when trying to remove the coil’s cable, and for whatever caused the jolt/shock I felt in my arm when I finally managed to haul the cable free of the socket.

Answer 1

The mechanical analog of this is water hammer. Or trying to stop a spinning flywheel. Or how the momentum behind a speeding train exerts no force on you until you try and slow it down or stop it.

Current is the momentum (mass with speed behind it) of the train or water. Voltage is the force (or impulse) exerted by that momentum the train or water when you put something in its way to slow it down.

The name is called inductive kick or inductive flyback.

When you send current through the inductor, the inductor will use the energy in that current to maintain a magnetic field. When the power source that was supplying the current through the inductor dissappears, the inductor tries to keep the current flowing through it the same and it does so using the energy stored in the magnetic field.

The inductor uses the energy in the magnetic field (which corresponds with the magnetic field collapsing as its energy is consumed) to maintain the current as close as possible to the same current levels as when the current source disappeared.

The inductor does this by becoming a power source using the energy stored in the magnetic field to produce a voltage as high as necessary to push that level of current through any obstacles so that the current flowing through the inductor is the same. If the easiest path is across the air gap of the open contacts of a mechanical switch or relay, the voltage required to spark across that air gap will be very high so that's the voltage that will be produced. That requires a lot of energy and the energy stored in the magnetic field is finite so the current will collapse to zero more quickly than it otherwise would.

For inductances, $V = L\frac{di}{dt}$. So to change the current very rapidly you must use a high voltage. But conversely, if you change the current very rapidly you will produce a high voltage. So if you make the current decrease very quickly (i.e. interrupt it) a very large forward voltage will be generated as the inductor tries to push and keep that same current going through the high impedance you just made.

The voltage that develops across a coil when you try to increase current through it is called the back EMF because it is resisting the flow of current from the voltage source.

The voltage that develops across a coil when you try to decrease the current through it is called the forward EMF because it is driving the flow of current through itself.

The sticking action you felt could have been the arc (a current being forced through the air as the inductor expends the energy in its magnetic field to keep pushing the current so it flows through the itself) welding the contacts.

Answer 2

Consider this circuit mimicking your lab situation.

You have a DC voltage source ($U=10 \text{V}$), a switch, a volt-meter, a really big coil (with a high inductance $L_\text{coil}=1\ H$, and a low resistance $R_\text{coil}=10\ \Omega$), and finally your body (with a high resistance $R_\text{body}=10\ \text{k}\Omega$, assuming you have dry fingers).

Now close the switch. The circuit will soon reach a steady state. The current through the coil will be $I_\text{coil}=\frac{U}{R_\text{coil}} =\frac{10\ \text{V}}{10\ \Omega} =1\ \text{A}.$ And the current through your body will be $I_\text{body}=\frac{U}{R_\text{body}} =\frac{10\ \text{V}}{10\ \text{k}\Omega} =1\ \text{mA}$ which is probably too small to feel it.

Now open the switch. The coil still carries the magnetic field energy. Therefore, in the moment just after switching off, the current through does not "want" to stop. Instead the inductance will induce a voltage just high enough to let the current ($I_\text{coil}=1\ \text{A}$) continue, but now flowing in the right loop counterclockwise through your body. That's why you feel a strong jolt, which can hurt you seriously.

Luckily for you, this current will exponentially die off with a short time constant $\tau=\frac{L_\text{coil}}{R_\text{coil}+R_\text{body}} =\frac{1\ \text{H}}{10.01\ \text{k}\Omega} \approx 0.1\ \text{ms}$.

You may want to run this in a circuit simulator. Especially notice the high voltage peak ($-10000\ \text{V}$) when opening the switch.