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Clearwater:
From the descriptions you have given I have no idea what you have said from a logical point of view.
Let me review.
You have a single phase main panel.
At this panel is a two pole 30 A breaker.
From this panel is a four conductor cable, red, black, white, and EGC (ground wire).
Red and black are connected to the breaker.
I assume white is connected to the neutral bus, and that EGC is connected to the ground bus.
This cable is 100 ft long and connects to a subpanel and I assume some more breakers.
There are 240 V motor loads, and 120 V light loads on the output of the subpanel.
You use a Fluke multimeter. You do not have or use a 10 ohm test load (an electric heater), or even a 100 W bulb.
It is not clear where you make your voltage measurements.
At the destination (subpanel) with all breakers on and the destination loads on you measure 123 V from ground or maybe it is neutral to one hot lead and 45 V to the other hot lead still using the same reference point (neutral or EGC). It is not clear that when these voltages are measured that the loads are connected, or on which side of the breakers the measurement is made.
From your post#1
Disconnect Red at both ends and checked voltage. Black was 123v and Red 45v. Also did Black test with same results. I had also checked all connections for corrorsion and found none and tighten all conections... no voltage change. With the circuit off, I got around .28v and .19v on the legs.
Apparently the red wire is your problem wire. In the paragraph preceding this quote you did not identify the 45 V with red.
Now you disconnect red at both ends and still read 45 V from red to the reference point. This means you did not have a load on red at the destination before you disconnected red at both ends.
At this point you should have put a load, 100 W bulb, from the red wire to neutral. The result would probably be zero volts.
What did "Also did Black test with same results." mean. Was the red reconnected and the black disconnected at both ends and black to neutral read 45 V, or did you mean something else?
I did not understand your continuity measurements. A reasonably valid test would be to disconnect both ends and apply a test current of maybe 10 A thru the wire of interest. 120 V and about a 10 ohm resistor would serve the purpose in your application.
Your shifting of wires and the results got me totally confused. You need to define points with names, the wire colors are unique and therefore those are good names, and where voltages are measured. A voltage has to be between two points.
A very useful tool in troubleshooting this type of problem is a common voltage reference point. like the EGC bus at the main panel. You can use a long wire or an extension cord to bring this reference point to a remote location. However, in your case you used either the neutral wire or the EGC at the subpanel for this purpose. This was probably OK, but it assumes that whatever that conductor was that it had good continuity and had no current flowing thru it.
As others have said you probably have an open in the red wire. You must provide a better description and additional tests to determine where your problems are located.
You have some knowledge of electrical circuits, and this troubleshooting operation will expand that knowledge. Changing loads on a circuit and observing the result can be a useful tool. Try it here.
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