What do these electrical wire colors mean, and what would the red tape indicate?
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The red tape is there to indicate that this wire is not neutral and should not be used for receptacles or light fixtures. It's also an indicator that there isn't a ground wire present.
The black sheath means it's a hot or live conductor, which carries the electricity to the device. The white sheath means it's a neutral conductor, which takes the energy away from the device and back into the system.
The bare copper ground wire conducts excess electricity away from any fire hazard.