But without a service manual and/or expert knowledge, there is no way to
determine what the value of the badly burned resistor may be.
As to the cause, any short in the circuit will cause a resistor to overheat
and burn up.
In electronics, there are just too many things that can cause a resistor to
burn up. (All of them bad!)
Without holding the circuit board in my hands, and tracing the circuit,
there is no way for anybody that does not have the service manual for the HP
Scanjet 5370C to tell you what the value of that resistor is.
If HP will sell you a service manual, that may the lowest cost way to find
the value of R105.
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