An unblown fuse is supposed to be close to a short circuit,which brings the voltage either side of the fuse to close to the same level.
When the fuse blows no current goes through the fuse, but current can still go through the rest of the circuit, so the voltage is only really pulled down by whatever current is going through the meter. As most meters have a very high input resistance when measuring voltage, the rest of the circuit usually conducts enough that you see close to your power supply voltage across a blown fuse.
Think about the circuit, 12v -> fuse -> incandescent lamp -> gnd. Normally the lamp is what’s limiting current, so the voltage across the lamp is close to 12v. If the fuse blows, it’s the fuse that’s limiting current, but electricity can still flow through the lamp, so the fuse side of the lamp gets pulled down to gnd.
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