Frayed wire?

I changed a light switch today. When the switch apparatus was pulled from the wall, I noticed that one wire seemed to be missing some rubber insulation. I could see a bit of the thin metal wire inside. What is the easiest way of repairing that? Duct tape? How much does one use?

I live in an old New York City building where old wiring coexists with new wiring. This looked like old wiring. The black rubber insulation is covered in a straw-like material -- perhaps that is extra insulation? Anyway, that stuff is a fright. I trimmed some of it away because it looked like a floozy on a bad hair day.

Should I be scared? We poets generally don't know much about the fine points of wiring.

Let me also mention that I was meticulous in connecting the wires to the new switch exactly as they were connected to the old switch. But the new switch is working differently. Yes, the two overhead kitchen lights go on, but this is a double switch, with two on-off levers, one for each light. Pressing just one lever lights both the lights. This is most perplexing.

 

Yes, that stuff is a problem,,, be careful and try to leave as much intact as you can. Duct tape is a no-no,, you might do the best you can with black elect tape and carefully re\install the switch folding wires in so they dont touch anything. There is a little tab on the side of that switch that needs to be broken out to seperate them,, one side only. If the switches are identical look at the old one.