Holiday lights are often connected in series and use special lamps that short out when the potential difference across a lamp increases to the line voltage. Generate an explanation why and explain why these light sets might blow their fuses after many bulbs have failed.

If there isn't this type of mechanism, the whole setup will blow even if only one lamp burns out. Doing this mechanism is to decrease the overall resistance resulting in an increased current (Since resistance and current are inversely related) which is the best to blast the fuse.

no. dot product   =0 when vecs at right angles