That resistor connects the transistor's base lead to ground. The base is the input. Voltages there are fairly low, and the current this will push through a 10-ohm resistor won't overheat it.
Until someone causes the RF transistor to fail. They tend to short between the collector and the base. The collector is the output side of the transistor, connected to the 12-Volt main power. This shoots 12, or 13.8 or whatever the power source is the wrong way out of the transistor's input side. Twelve volts applied to a 10-ohm resistor will release 14.4 Watts of heat. Naturally, the half-Watt resistor in the pic gets toasty from a 28-to-one overload factor.
The real news is the cost and risk of replacing the transistors. The resistor alone is the cheap part of any real repair.
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