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 2.05 mm extends directly upward by 0.831 km and is coated with a 0.511 mm layer of water having resistivity 151 ohm middot m. If the potential difference between the two ends of the string is 175 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). Number Units the tolerance is +/-1 in the 3rd significant digit

Explanation / Answer

here,

radius , r = 2.05 * 10^-3 m

x = 5.11 * 10^-4 m

length , l = 831 m

V = 175 MV

V = 175 * 10^6 V

the current through the wire , I = V/R

I = V * area /( p * L)

I = 175 * 10^6 * pi *((r + x)^2 - r^2) /( 151 *831)

I = 175 * 10^6 * pi *((2.05 * 10^-3 + 5.11 * 10^-4)^2 - (2.05 * 10^-3)^2) /( 151 *831)

I = 1.03 * 10^-2 A

the current through the wire is 1.03 * 10^-2 A

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