Torn MagSafe 2 Power Adapter 45W
MacBook Air (13-inch Mid 2012), null
MacBook Air (13-inch Mid 2012), null
You should buy a new power adapter from Apple.
Best.
Am I not able to use this cable then?
I wouldn't, your Mac is worth a lot more than a new charger costs. Take it to Apple, they may give you a new one, if not you'll be in the right place to buy a new one.
Am I able to put electrical tape on it?
Look, it's your stuff, you can do whatever you want. I however would replace it.
order new cable from ebay and replace broken with it using youtube instruction
Avoid using non-sanctioned Apple electrical products. I believe there was an incident of an electrical fire last year. As I recall, this was a case of an iPhone charging with a non-sanctioned charger and/or cable.
As all but cabakroll have advised you, use only Apple gear to charge your Apple equipment.
OWC offers GENUINE Apple chargers at a modest discount.
https://eshop.macsales.com/search/magsafe
Do not fool with the charger that you have. Replace it.
Ciao.
Torn MagSafe 2 Power Adapter 45W