Question

Chapter 26, Problem 022

Flying Circus of Physics

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 2.19 mm extends directly upward by 0.826 km and is coated with a 0.519 mm layer of water having resistivity 170 ?·m. If the potential difference between the two ends of the string is 177 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).

Answer 1

On assuming that the kite string has negligible conductance,

Therefore, Resistance = Resistivity * length / Area

Considering the cross-section of the string with water coat. The string is having a radius of 2.19 mm, so the water layer is starting at 2.19 mm and goes to 2.709 mm.

The cross-sectional area of conductor is thus a "water like concentric circle and its area is

A = *(2.709 x 10^-3 m)²- (2.19x 10^-3 m)²= 7.98 x 10^-6 m²

= 170 * 826 / 7.98 *10^-6 = 1.75 * 10 ¹⁰

Further, Applying Ohm's Law,

I = V/R

(V = 177 mV = 177 * 10 ⁶V )

I = 177 *10⁶/ 1.75* 10 ¹⁰ = 1.01*10^-2 A

  

answered by: anonymous