When you plug in a power supply or close a contactor, the instantaneous current can be 10 to 100 times the steady-state value. Bulk capacitors look like a short circuit at t=0, and transformers with low primary DC resistance behave the same way. That spike pops fuses, welds relay contacts, sags the upstream bus, and stresses bridge rectifiers — often killing them on the third or fourth power cycle rather than the first.

The classic fix is an NTC thermistor in series with the input. Cold, it presents 5-50Ω and limits the surge. As current flows, self-heating drops its resistance to a fraction of an ohm within seconds, minimizing steady-state losses. Cheap, no control circuitry, used in nearly every PC power supply.

The catch: NTCs only work after they've cooled down. Cycle power quickly and the thermistor is still hot (low-resistance), giving you no protection on the second turn-on. They also dissipate real power continuously — a 5Ω NTC carrying 3A burns 45W steady-state if it didn't self-heat. Don't use them on hot-swap or frequently-cycled equipment.

For better behavior, use an active inrush limiter: a power resistor in series with the load, bypassed by a relay or MOSFET after a delay. The resistor absorbs the surge for the first 50-200ms, then the bypass switch shorts it out. Energy in the resistor is bounded by ½CV² — a 1000μF cap charging to 400V dumps 80J into the resistor, so size it for that single-shot energy, not continuous power.

Calculation: For a capacitor C charging through resistance R from voltage V, peak current is V/R and the RC time constant is τ=RC. Pick R so peak current stays below your fuse/diode rating. Example: 470μF bulk cap, 325V peak rectified (off 230VAC), 10A diode bridge. Need R ≥ 325V/10A = 33Ω minimum. Charging energy dumped in R equals ½CV² = ½(470μF)(325V)² = 25J — pick a 25W wirewound rated for that pulse energy, then bypass it after 5τ ≈ 80ms.

Real-world example: Industrial VFDs (variable frequency drives) almost universally use the precharge-resistor-plus-bypass-relay approach. When you energize a 10kW drive, you're charging a DC bus of several thousand microfarads to 565VDC. Without precharge, the inrush would trip the breaker every time and weld the input contactor closed within a few cycles. The drive logic closes the bypass contactor only after the DC bus voltage reaches ~90% of nominal, confirming the precharge completed safely.

For low-voltage hot-swap (12-48V), an inrush-limiting MOSFET in linear mode is cleaner — drive the gate slowly with an RC network so the MOSFET turns on over milliseconds, controlling dV/dt on the downstream capacitor. Watch the SOA (safe operating area) curve carefully: the MOSFET dissipates V_DS × I during the ramp, and that pulse must fit under the SOA line.