MRI magnets and other magnets that have a low current and high self-inductance are passively quench-protected with a system that includes sub-divided coils with resistors and diodes that are in parallel with sections of the coils. The primary purpose of coil sub-division is to protect the coil from the high voltages that can occur during a quench. In the event of a lead failure (conventional or superconducting) between the coil and its power supply or its persistent switch, the total current in the coil flows through the diodes and resistors in parallel with the coil. When a lead fails, the current decay time constant for the coil current can be quite long. It is desirable that the coil quench in a time that is short compared to the coil current decay time constant. Experience shows that the heating from the resistors and diodes will eventually quench the magnet. This paper presents methods for shortening the time between a lead failure or a persistent switch failure and the eventual magnet quench. © 2011 IEEE.