# Would the empirical behavior of a simple circuit match my model of it?

I have a practical problem in E&M which has baffled me and and my electrician. The copper water pipes in my house are carrying a current of small potential (~1V) AC current. Here is my hypothetical circuit diagram:

         R1     R2
~~---o------+--------+
|           |        |
| R3      source   ground
|                    |
+--------------------+


Where o is my shower head and ground is actual ground from which the supply pipe enters the house. R1 and R2 represent the assumed (low) resistances of the copper piping. The way I detected the current was while changing a light fixture above the shower head and detecting a flow from my showerhead to the grounded junction box through my forearm. This current produced a mere tingle in my arm and has been confirmed with two different multimeters: my "toy" and the electrician's Fluke. R3 represents my arm, an intermittent connection to ground.

There is also a 2m copper ground spike embedded in the outside earth connected to nothing which can be used as a reference. The common/neutral line of the breaker box is currently tied at R2 near where the municipal supply line enters the house's basement. The source is unidentified but assumed since there is a measured, felt potential on the copper pipe.

If the circuit is how I have drawn it, I believe the following would be true following Maxwell, Ohm, and/or Volta:

1. in the typical case with R3 disconnected all current goes from source to ground via R2
2. while my arm is touching the pipe and the grounded junction box, most of the current goes from source to ground via R2 while a small current goes through R1 and R3 where R3 is presumed to be of much higher impedance than R2.

Is this a correct interpretation of how the hypothetical circuit would behave?

For the curious, the house is 80-ish years old with some olde-fashioned knob-and-tube (poorly insulated) wiring inside the walls that we guess could be in contact with the plumbing and thus be presumed current source.

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