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 2.13 mm extends directly upward by 0.811 km and is coated with a 0.516 mm layer of water having resistivity 150 Ohm middot m. If the potential difference between the two ends of the string is 166 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

V = I R

I = V / R

R = L / A

where A = ( r2^2 - r1^2 )

L = 0.811 lm = 811 m

r2 = r1 + r

r = 2.13 mm

r = 0.516 mm

r^2 = ( r1 + r )^2 = r1^2 + 2r1r + (r)^2

r2^2 - r1^2 = 2r1r + (r)^2 = (2r1 + r)(r)

R = L/ [(2r1 + r)(r)]

2r1 + r = 2(2.13 mm ) + 0.516 mm = 4.776 mm

= 4.776 x 10^-3 m

r = 0.516 mm = 5.16 x 10^-4 m

(2r1 + r)(r) = ( 4.776 x 10^-3 m)(5.16 x 10^-4 m )

= 2.464 x 10^-6 m^2

R = ( 150 -m ) ( 811 m ) / [ ( 2.464 x 10^-6 m^2)

R = 1.5724 x 10^10

I = V / R

I = 166 x 10^6 V / 1.5724 x 10^10

I = 105.57 x 10^-4 Amp

I = 10.557 mA

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