PHYSICS Current and Resistance

Question

Measurements made during severe electrical storms reveal that lightning bolts can carry as much as 30 C of charge and can travel between a cloud and the ground in time intervals of around 100 s (and sometimes even shorter). Potential differences have been measured as high as 400 million volts.

1.What is the current in such a lightning strike? 

2.What is the resistance of the air during such a strike?

3.How much energy is transferred during a severe strike? 

4.What mass of water at 100 degrees (Celsius) could the lightning bolt in part (3) evaporate? The latent heat of vaporization of water at 100 degrees (Celsius) is Lv=2260 kJ/kg. 

Answer 1

1. Current is defined as rate of flow of charge. Use the following equation

I = Q/t I = current Q = charge t = time

I = 30/(100 x 10^-3) The question says 100s, but that is a lot of time for lightning. Please check the original statement carefully. I will solve this and following parts using t = 100ms which is more realistic.

I = 300A

2. The equation for Ohm's law is

V = IR

400 x 10⁶ = 300R

R = 1.33 x 10⁶Ω

3. Electrical energy is given by

E = VIt

E = 400 x 10⁶ x 300 x 100 x 10^-3

E = 12 x 10⁹J

4. Energy and latent heat are related by the equation

E = mL_f

12 x 10⁹ = m(2260 x 10³)

m = 5310kg