I believe the ohm's law you are using applies only to DC circuits. Search Ohm's law for AC circuits.

What makes you think the control bank fires for that long? Most momentary solenoids are less than 50ms

Why is there air?

Well, if we're going to discuss why a fuse doesn't blow, I figured we could discuss other more existential topics?

This is a great question! I hooked up an A-5196 coil to 120 VAC through a meter that measures AC amps. The passive resistance of the coil I used is 13.6 ohms. When I power up the coil for five seconds, I get a reading of around 6.8 amps. This reading is not exact because as the coil heats up, the reading changes. I didn't keep the coil on for very long because that is a large amount of current draw and I didn't want to burn up the coil.

We might expect to see: 120 volts / 13.6 ohms = 8.8 amps

But what we saw was: 120 volts / 17.6 ohms = 6.8 amps

I am going to assume that the "extra" 4 ohms of resistance is due to the impedance generated by running AC through an inductive load.

When I put a 5 amp fast-blow fuse in the above circuit, it did not blow after being on for 5 seconds, although I could see the fuse link starting to sag. When I put a 1 amp slo-blo fuse in the above circuit, it took about 1/3 of a second (333 mS) to blow.

So I think the above posts are correct - the current draw is less than you would expect from the passive resistance measurement, and the fuses don't blow due to a combination of the overload not being large enough and the short amount of time that the coil is on.

We can also rest assured that if the reset coil ever gets locked on, the 1 amp slo-blo fuse will go very quickly, which will prevent the coil from burning up, and also keep the 5 amp fuse from eventually blowing.

- TimMe

Here's a few things that matter beyond the simple form of Ohm's law (V=IR)

- Faraday's Law of induction

- Lenz's Law

- Impedance

There are other things that matter but these are biggies.

And the characteristics of the coil change drastically when it has a plunger within it and where the plunger is positioned in the coil.

I am not an electrical engineer, but I know there are ones here who can go into far greater detail about this and will probably correct my inaccuracies but I'll give it a shot in very basic terms...

The total amount of opposition to current flow is called impedance. Impedance is resistance and reactance added together. We get reactance in AC circuits where the current is constantly changing due to the sinusoidal wave that is the nature of AC power. Lenz's law tells us that this change in current in an inductor is opposed, that opposition is known as inductive reactance. Inductive reactance grows as our frequency grows.

In addition to that we have Faraday's law that tells us we will be generating back EMF that will oppose our current flow. The amount of back EMF will have to do with the size and number of turns of our coil.

So, your ohm meter measures only resistance, not impedence. Since I doubt you have an impedence meter the easiest way to know the total impedence is to measure the voltage and current and plug them into this form of Ohm's law: V=IZ (Z being impedence) .

This is why your current is not as high as V=IR would tell you, and why your fuse doesnt blow.

I'd have to agree with this as the biggest issue with Rolf's "fault in thinking". The inrush current is happening faster than you think, on average - 26 ms. The use of a time delay fuse is selected on the basis of preventing nuisance blows during equipment start up. In a pinball machine the value selected for the solenoid fuse isn't super critical, it just has to be sufficiently below the current capacity of the wiring/coils to open up when the solenoid is stuck on.

You also need to understand that very often the tolerance for fuse values is "as high as" 50%.

Fuses are a mechanical device NOT an electrical one.