Extension cords, when improperly used, will fail. Small extension cords are appropriate for lights or alarm clocks but not appliances or power tools. Length also is important. Long cords that are undersized lose power and overheat. Eventually, these cords melt or blow out at their plug connections. Blown extension cords are serious fire hazards. It's OK to repair the cord with a replacement connection, but do not reuse it for the same application. Replace the cord with a heavier one.
Things You'll Need
Disconnect the damaged plug from the electrical outlet. Use wire strippers to cut off the blown connector, and strip 1/2-inch of insulation off of the end of the wires. If the wires are molded together, the two side-by-side wires supply the main power. The third wire, separate from the others, is the ground circuit. If the cord is not molded and the wires are separated and color-coded, the black and white wires supply main power, and the green is ground.
Open the replacement connector. Inside are attaching screws that connect the wires from the cord. Follow the length of the molded cord to the intact end, and straighten and orient the cord to fit the new connector. Without color codes, orientation is important. Otherwise the connector will be installed upside down. Use a screwdriver, and install the properly oriented wires in the connector. Install colored wires according to screw colors; white to the bright screw, black to the gold screw and green to the green screw.
Close the cover of the repaired electrical plug. Do not reuse the cord on the same application where too much current draw caused it to fail.
If you are concerned about your extension cords, a quick test, although not entirely accurate, is to feel the cord. If it feels the slightest bit warm, replace the cord with a heavier one. A better test is to determine the amperage needs of the circuit. Small cords are only rated to carry 10 amps, but this drops the longer the cord. A 1,500-watt blow dryer easily exceeds this amperage. If you feel uncomfortable disconnecting a blown extension cord, turn off the circuit breaker or wear rubber gloves when pulling out the plug.
110-volt circuits are dangerous when improperly used. Properly size the cord for correct usage, and never work with live circuits.