App note from ON Semiconductors on how eFuse manage to cope up with large capacitive loads. Link here (PDF)
The eFuse protection devices are used for limiting the system load current in the events of overload or short circuit. Many applications employ On Semiconductor eFuses at the power input stage of the system between the main power input connector and DC−DC converters or power regulators. The systems utilizing eFuse protection devices at the power input stage may represent inductive, resistive, capacitive or mixed types of loads.
One of the common load characteristics for various systems is large capacitive load, typically starting from 1mF all the way to few hundred milli Farads. The challenge presented by such load to an overcurrent protection system is large inrush current due to the excessive capacitance which will cause the device to shut down during startup.