Kiting during a storm . The legend that Benjamin Franklin flew a kite as a storm

Question

Kiting during a storm. The legend that Benjamin Franklin flew a kite as a storm approached is only a legend — he was neither stupid nor suicidal. Suppose a kite string of radius 2.33 mm extends directly upward by 0.817 km and is coated with a 0.508 mm layer of water having resistivity 169 ·m. If the potential difference between the two ends of the string is 184 MV, what is the current through the water layer? The danger is not this current but the chance that the string draws a lightning strike, which can have a current as large as 500 000 A (way beyond just being lethal).

Explanation / Answer

Resistance = resistivity x L /A

A = cross section area of water layer

A = pi [(2.838 x 10^-3)^2 - (2.33 x 10^-3)^2 ] = 8.25 x 10^-6 m^2

L = 0.817 x 10^3 m

R = 169 x 0.817 x 10^3 / (8.25 x 10^-6)

R = 1.674 x 10^10 ohm

I = V/R = (184 x 10^6) / (1.674 x 10^10) = 0.011 A

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