Thanks for the clear explanation, but there is one thing I cannot get my head around.
Isn't the quickest way of dissipating energy in a coil by a short circuit across the the coil (like a diode). I would have thought that a higher resistance across the relay coil would take longer to dissipate the energy in the coil. This is the bit that I do not understand.
It is a conundrum, because I accept that putting a resistor in series with the diode is recommended practice in some areas, as you say.
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The coil has a high inductance. The voltage across the coil is the inductance times the rate of change of current. If the decaying coil current goes through a diode only, the only resistance in the way of the current is the coil resistance, so the current decays slowly. If there is a big resistance in series, the voltage is larger and the current decays faster.
If there is no resistor, the rate of change of current is huge, so the voltage is huge, and that does damage to whatever was trying to turn the circuit off.
Some figures. A 12 V automotive relay takes around 50 mA, so has a resistance of 240 Ω. It will take about 5 ms to turn on, so the time constant is about that, so the inductance is around 1 H. If there is no series resistance, the current will decay with the same time constant. The initial rate of change of current is 12 A/s
If there is a series resistance of 2400 Ω, the relay current of 50 mA will initially be the same and will generate 120 V across the resistor, and therefore across the coil. The rate of change of current is 120 A/s. The coil energy mainly ends up in the resistor.
Using just a diode is a very good way of dissipating the energy, if you don't care how slowly the relay turns off. The coil power is no bigger while turning off than when running, and the peak voltage on the switching device is only 0.7 V bigger than the supply, so it is very good to the rest of the circuit. It is the contacts that can suffer.
And most off-the-shelf AC snubbers have relatively high value resistors in series with the capacitor.
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That can stop unintended resonance with the coil, and it can stop a large current inrush to charge the capacitor, which can be as harmful as a voltage surge when trying to turn off the coil.