As John has posted the 25 ohm resister is indeed part of the alternator excitation circuit. It serves a dual purpose. It protects the electrical system if the connection should fail between the battery output stud on the alternator and the battery. If that were to happen all the charging current would flow back through the #1 terminal to the ignition switch. The small wires in that circuit are not designed to carry charging current. It also add a resistance in that circuit so that the alternator does not back feed the ignition switch and prevent the engine from being shut off.
As long as you are not having problems shutting off the engine the 1.8 ohm resistor you replaced it with will function OK but you have lost some of the circuit.
The battery circuit failure is not very common. In 40 plus years of working on tractors I ran across it for the first time last summer. The battery lead had broken in the harness near the alternator creating an open circuit. The charging current flowing through the 25 ohm resistor had also burned it out. Since the customer had already replaced the alternator I do not know if it too had been damaged but the replacement unit would not start to charge due to the open resistor.
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Today's Featured Article - Identifying Tractor Noises - by Curtis Von Fange. Listening To Your Tractor : Part 3 - In this series we are continuing to learn the fine art of listening to our tractor in hopes of keeping it running longer. One particularly important facet is to hear and identify the particular noises that our
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