1) SE cable prior to 1996 was used as a dual purpose cable for Service Entrance wires from the utility connection or also installed internally inside the home for range, cooktop and/or electric dryer branch circuit wiring. Thus there are 4 possibilities on the use of SE cable. Today's code only allows the use of SE cable from the utility service connection to the electrical panel and can no longer be used for ranges, cooktops or dryers if the circuit was installed after 1996.
2) After 1996, the code required a 4 wire system for such appliances which now requires a 4 wire system comprised of 2 insulated hots, 1 insulated neutral and 1 equipment ground. Take a look at the exterior insulation of your branch circuit. If it is labeled as type SE (Service Entrance cable) then you can connect the 4 wire cooktop to the 3 wire SE cable.
If the branch circuit wiring is not SE cable, then it is a code violation and it will create a potential fire hazard to use the bare copper wire as a neutral conductor. Only SE cable is allowed to use the bare wire as a neutral. No other cable types are permitted to use the bare wire as a neutral as they must now be an insulated neutral conductor.
3) Back in the day, many electric ranges and cooktops only required 240 volts and did not require a neutral conductor. Now days, most ranges, oven and cooktops require a combination of 120 and 240 volts. Thus the reason for the neutral conductor to provide the 120 volts.
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