Inrush Limiter (NTC) Sizing
Cold resistance to cap the surge into a capacitor bank, and the joules the NTC must swallow.
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The engineering
Worst case is honest and simple: switch closes at the mains peak into a discharged bank, and the only thing between the line and a dead short is the limiter's cold resistance — so R_cold is just V_peak over your allowed surge. The second row is the deeper spec: while charging a capacitor through *any* series resistance, the resistance dissipates exactly as much energy as the cap stores (½CV²). Pick an NTC whose energy/joule rating and rated capacitance meet or beat those numbers, not just the resistance.
The NTC's trick is that it gets out of its own way — self-heating drops it from tens of ohms to tenths — but that's also its trap: a hot NTC gives near-zero protection during a brief power blink, since it needs tens of seconds to cool. Gear that must survive rapid re-strikes uses a relay or triac to bypass (and cool) the NTC, or a resistor-plus-bypass precharge circuit; check the surge against the device's I²t rating for repetitive duty.
Where this math comes from
The NTC effect is nearly as old as electrochemistry — Michael Faraday noted in 1833 that silver sulfide conducts *better* hot, the first recorded semiconductor behavior, a century before anyone could use it. Bell Labs turned the curiosity into a component: Becker, Green, and Pearson's 1946 paper 'Properties and Uses of Thermistors' introduced reproducible oxide thermistors from wartime work.
Inrush limiting became the thermistor's mass-market job when off-line switch-mode supplies (1970s onward) put hundreds of microfarads directly behind a bridge rectifier — every PC, TV, and wall-wart since has a small black disc paying this card's ½CV² toll at every cold start.
- 1833Michael FaradayNegative temperature coefficient observed in Ag₂S — the first semiconductor effect.
- 1946Becker, Green & Pearson (Bell Labs)'Properties and Uses of Thermistors' — the modern NTC component.
- 1977Off-line SMPS eraRectifier-fed bulk caps make NTC inrush discs ubiquitous, circa.
See the full timeline of the math behind every calculator →
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