A thunderstorm with a potential difference of ten million Volts between two clouds produces a lightning stroke of ten thousand Amperes at its peak with a rise time of tenmicroseconds and a fall time of one hundred microseconds. How many Coulombs does it carry? What are the peak power and the total energy of the lightning stroke?

Answer 1

we need to find the total charge passed during the rise and fall
during rise
i = {10^4amps /[10^-5 s]}t
area under that line (the triangle) is in coulombs
Q = .5*10^4*10^-5 = .05 Coulombs

during fall
Q = .5*10^4 *10^-4 = .5 Coulombs

peak power = volts * peak amps
10^7 * 10^4 = 10^11 watts (yikes)

total energy = integral of Vi dt assuming V is constant that is V int i dt
but we know integral i dt = .05 + .5 =
.55
so 10^7 Volts * .55 coulombs total energy