On old electronics that don't have a polarized power cord, what would be the benefits of adding a 2.2Mohm resistor from one side of the a/c to the chassis and switching out to a polarized cord (specifically on a vintage receiver)? A stereo tech recommended it to help eliminate a ground loop but I don't understand why.
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Old Audio equipment used conventional AC transformers to isolate and protect users from high voltage. Is also improved CMRR of the high impedance phono inputs IF the transform also had low leakage. The capacitive coupling or leakage at 50/60Hz may introduce hum if another AC powered device such as a turn-table generated common mode stray hum and the combination of the two may permit nuicance hum in the phono pickup.
In some cases the coupling of AC may be more pronounced on the line or neutral side depending on winding style so simply reversing the plug would determine if this is the case.
If hum is not a problem, there is no advantage to grounding the unit and for long wires there is more of a risk due to ground faults in residential and commercial installations, meaning that you might get a shock connecting a long coax plug holding onto the sleeve and destination case.
If hum still is a problem after reversing the plug, then shunting the stray floating CM AC magnetic fields with a lower impedance such as 1Mohm resistor may help a bit but it might be better to use ferrite CM chokes for the cable to pass thru such as those used on VGA cables and DC charger cables or better, specifically rated for high permeability and low frequency.
If equipment, whether old or not, has a unpolarized plug, leave it that way. In fact, don't mess with anything related to that. Each piece of equipment was designed a particular way. You don't know all the design criteria that went into it, tradeoffs made, and possibly parts of the unit relying on it being as designed. Leave it alone, whether polarized or not, old or new, 3 prong or 2 prong.
This is especially true if you let others use something you have modified. If they get hurt from it electrically in any way, the blame will be on you. This has nothing to do with whether your modification was the cause or not. If I was on the jury, I'd probably not believe you did only what you say you did. Now imagine how a lawyer would hype this to people who don't know anything about electricity. You open it, you own the liability.