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Replacement parts for Roper REX4625EW1 DRYERS | AppliancePartsPros.com

See the attachment for the tech sheet. The closest I could find was an REX4625EN0. Yours should be a close match if not the same.

The unit does not measure the moisture directly in auto modes.
What it does is that timer contacts TM/OR close. The timer motor then gets power through the heating coil when the coil is turned off by a thermostat. The resistor drops the 240 volts down to 120 volts which is what the timer motor requires.

Unplug the unit and set it to mid scale in an auto mode.
Measure the TM/OR timer contacts. Should be 0 ohms.
Measure the resistor. Should be about 4,500 ohms.
Disconnect both wires from the heating coil. Measure the coil. Should be about 10 ohms. Then measure from each side of the coil to the frame. Both should be infinite ohms (open). What can happen here is that the coil can ground and it is running on 120 volts so the timer motor never gets the correct voltage in auto mode.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.

There is a good STICKY at the start of this forum about it's use.