When connecting two wires can glue be used and still have an electrical current pass through the wires?

You would have to be crazy to do this. Go to your local hardware store and buy connectors made for the purpose. Only make connections inside an electric box, not just at random places in a cable. Make sure to turn off power before doing this. Both wire nuts and push type connectors are available in any hardware store.

If wires are lower current in an appliance or devise you may be able to solder and tape or use heat shrink tubing.

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