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The dropping resistor works with duty solenoid A in regulating the automatic transmission fluid line pressure. This resistor keeps a certain amount of current flow through duty solenoid A during the 'OFF' portion of its duty cycle. So in other words, duty solenoid A is never fully 'OFF'.
If this resistor fails open, becomes disconnected, or has its wiring severed, one result might be increased shift shock. The reasoning behind this is that without the resistor in the circuit, the line pressure may be higher, since without the current passing through solenoid A during the 'OFF' portion of its duty cycle, it will tend to close further, and thus not bleed off as much pressure from the automatic transmission fluid pump.
If the resistor fails open or is disconnected, it should cause the ATF temperature lamp to flash 16 times on the next startup, since the TCU would be able to see electrically that the resistor is open.