I've been wondering this, if an eel was continuously shocking someone, would they sustain electrical burns as if they touched a high tension power line due to the high voltage and amps?
In the electric eel, some 5,000 to 6,000 stacked electroplaques can generate a shock of up to 860 volts and up to 1 ampere of current (1). They can also concentrate the discharge by curling up and making contact at two points along its body. When agitated, they can produce these intermittent electric shocks over at least an hour without tiring. Eels have been known to jump out of the water to shock prey or dissuade threats in the air (2).
A shock from an electric eel is like the brief, numbing jolt from a stun gun. Normally, the shock can't kill a person. However, the eels can cause heart failure or respiratory failure from multiple shocks or in persons with underlying heart disease. More often, deaths from electric eels shocks occur when the jolt knocks a person in the water and they drown.
Electrical injury is the physiological reaction caused by electric current passing through the body, electrical burn is a specific subset of that. For high voltage (above 500V) damage can be very severe but most of the damage occurs bellow the skin. If the voltage is less than 200 V, then the human skin, more precisely the stratum corneum, is the main contributor to the impedance of the body in the case of a macroshock—the passing of current between two contact points on the skin. The characteristics of the skin are non-linear however. If the voltage is above 450–600 V, then dielectric breakdown of the skin occurs.(3) Whether an electrical burn occurs is not always clear cut in the case of electrical injury and will depend on the conditions of the skin (perspiration etc).
It is possible for an electric eel to harm a human even when out of the water. The extent of the harm will depend on the exact voltage, current, hertz, pulse duration, and number of contact points between the eel and human. Whether this harm will included electrical burns depends on further factors and is particularly difficult to answer if you limit 'burn' to injury with a visible skin defect.