Final answer:
You are not injured by a spark of static electricity because the duration of the spark is too short to transfer a harmful amount of energy. Static electricity typically involves a discharge over a very brief period, meaning the total energy delivered is minimal and not harmful. This is in contrast to a sustained electrical discharge, like a short circuit, which can cause significant danger due to sustained high power delivery.
Step-by-step explanation:
A spark of static electricity may carry a few hundred watts of power, yet you are not injured by such a spark primarily because b) The duration of the spark is too short. Although a spark can indeed have a high power rating, the amount of energy delivered during a spark is very small due to its extremely short duration. Another way to understand this concept is to compare the spark to a powerful light bulb which might also have a high power rating; however, if the bulb only flickers on for a microsecond, the total energy delivered is minimal. Hence, static electricity typically doesn't cause injury because it doesn't have enough time to deliver a dangerous amount of energy. In contrast to static sparks, a short circuit in household wiring can cause significant danger as it can deliver a high power over a sustained period, leading to overheating and potentially starting a fire.
It's important to recognize the distinction between high power and high energy. Energy is the total amount of work done, and it's the product of power and time. Since static electricity discharges occur over such brief periods, the total energy accumulation doesn't reach levels that are harmful to us. That's why we don't get hurt from static shocks: the quick discharge time limits the energy transfer. This is the same reason why static electricity is not typically dangerous in everyday scenarios, including when we discharge static before pumping gasoline or when touching metal objects after walking on a carpet.