Precharging a variac or power transformer to reduce / eliminate excessive inrush current
The following might help if you are experiencing these issues.
Here's what I believe causes the inrush current and how I like to target the problem. The circuit being switched on has it's static magnetic "particles", if you will, scattered randomly instead of perfectly lined-up as in normal operation. If the particles are sitting the "wrong way" during start-up, they would first need to be turned around so they can "lock-in " with the rest of the gang. During this transition from random to lined-up the current could easily exceed 8 times the full load current of the winding. So if you have an 8 amp variac for example, you might see over 60 amps of inrush current. This large current would likely exceed the 20 amp breaker you're plugged into. Huge third harmonic content created during this transition doesn't help maters either. So bammm, your breaker trips or the fuse blows.
Here are three possible solutions, some practical, others not so much:
Zero Crossing Detector. As the term suggests, closing the switch when the voltage applied is at precisely zero crossing would be ideal. This concept is used in some high powered, high voltage circuit breakers. It's expensive to apply, requires reference voltage and knowledge of "how fast" the contacts need to close to be properly implemented. Too much for the DIY guy.
Input Current Limiting Resistance. Great for small inductive loads. Examples would include large wattage power resistors, incandescent light bulbs, etc, Downfall is if there was instantly full load applied and the resistors are not removed from the circuit in a "reasonable" amount of time, the resistor might catch on fire due to excessive power dissipation. This method is quite popular and often used---In my opinion it works, but it's not the best option.
Magnetic Precharging. As the name implies, the "scattered magnetic particles" are first lined-up at a low level of current before the main contact is closed. I do this with large variacs and plate transformers that are troublesome contact burning, breaker tripping SOB's. I use a run capacitor (the kind used in refrigeration A/C units) to effectively "precharge" the iron core. Use the same circuit as in example above, but change the resistor out in favor of a run capacitor. This series capacitance is usually dropped out with a bypass contact within a second or so. The advantage of this compared to using a resistor is the capacitor doesn't get hot yet produces the desired result of energizing the variac without nuisance breaker tripping.
Conclusion: Replace the resistor in the second example with a run capacitor and you're all set.