A person in bare feet is standing under a tree during a...

A person in bare feet is standing under a tree during a thunderstorm, seeking shelter from the rain. A lightning strike hits the tree. A burst of current lasting $40 \mu$ s passes through the ground; during this time the potential difference between his feet is $20 \mathrm{kV}$. If the resistance between one foot and the other is $500 \Omega,$ (a) what is the current through his body and (b) how much energy is dissipated in his body by the lightning?

Key Concepts

Ohm's Law

Ohm’s Law is a foundational principle in electrical circuits that states the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. This relationship is typically written as I = V / R, where I is the current, V is the voltage, and R is the resistance. It is used to determine any one of these quantities if the other two are known.

Joule Heating

Joule Heating describes the process by which the passage of an electric current through a conductor produces heat. The power dissipated as heat in a resistor can be determined by the expression P = I^2R (or alternatively, using the voltage, P = V^2/R). When the current flow is transient, the total energy dissipated can be computed by integrating the power over the time during which the current flows, typically using E = I^2R t, where t is the duration of current flow.

Transient Electrical Analysis

Transient Electrical Analysis involves studying circuits during conditions that change with time, often for short bursts or pulses of current. In transient events, such as a brief lightning strike, the time factor is critical for accurately determining the energy dissipated by the circuit components. This analysis takes into account the duration during which the electrical effect lasts, emphasizing that even a short duration event can have significant instantaneous effects.

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