I've been reading about self-inductance in circuits in M. Purcell's Electricity and Magnetism and came across an interesting fact:
"What happens if we open the switch after the current $I0$ has been
established, thus forcing the current to drop abruptly to zero? That would
make the term $L dI/dt$ negatively infinite! The catastrophe can be more
than mathematical. People have been killed opening switches in highly
inductive circuits. What happens generally is that a very high induced
voltage causes a spark or arc across the open switch contacts, so that the
current continues after all."
What do they mean exactly by highly inductive circuits? If I have a small circuit with a coil as an inductor, a battery with 2.3V and some resistance R, and if I open the switch after a long time, will there be an electric arc? Or this applies only to circuits with really high voltages and currents?
I mean, the mathematical equations still apply here and $dI/dt$ will be very negative when the switch is opened.
Best Answer
As you slide the switch open, it doesn't instantly transition from zero resistance to infinite resistance. As the contact area decreases the resistance rises, which acts upon the current to produce a voltage operating against the current. Even when the contact resistance becomes zero, there is capacitance across the gap, which produces a rapidly rising voltage, again operating against the current. If this voltage rises fast and high enough (which depends on the current and induction) then you will get a spark.
You can get a spark from a 1.5V alkaline D cell if you connect and disconnect a reasonable inductor to it.