How can I repair cable on my hedge strimmer that I cut through by mistake?

If you're confident with small hand tool you might consider either replacing the whole cable or if the damaged cable is close to the trimmer just shortening the cable, alternatively...

My trimmer suffered this and I just bought an in-line waterproof plug and free-socket from a DIY store and joined them to the respective ends of the cable - Exposed pin connector joined to trimmer and covered socket to the wire with the regular plug on it.

I now use the trimmer with the cable draped over my shoulder to avoid more damage.

Good luck...

Peccavi
May 2009