A thunderstorm with a potential difference of ten million Volts between two clouds produces a lightning stroke of ten thousand Amperes at its peak with a rise time of tenmicroseconds and a fall time of one hundred microseconds. How many Coulombs does it carry? What are the peak power and the total energy of the lightning stroke?
we need to find the total charge passed during the rise and fall
during rise
i = {10^4amps /[10^-5 s]}t
area under that line (the triangle) is in coulombs
Q = .5*10^4*10^-5 = .05 Coulombs
during fall
Q = .5*10^4 *10^-4 = .5 Coulombs
peak power = volts * peak amps
10^7 * 10^4 = 10^11 watts (yikes)
total energy = integral of Vi dt assuming V is constant that is V int i dt
but we know integral i dt = .05 + .5 =
.55
so 10^7 Volts * .55 coulombs total energy
To calculate the number of Coulombs carried by the lightning stroke, we can use the formula Q = I * t, where Q represents the charge in Coulombs, I represents the current in Amperes, and t represents the time in seconds.
Given that the current at the peak of the lightning stroke is 10,000 Amperes and the rise time is 10 microseconds (10 μs), we can convert the rise time to seconds by dividing it by 1,000,000 (since there are 1,000,000 microseconds in a second). So the rise time in seconds is 10 μs / 1,000,000 = 0.00001 seconds.
Using the formula, we can calculate the charge carried by the lightning stroke during the rise time: Q_rise = I * t = 10,000 A * 0.00001 s = 0.1 Coulombs.
Similarly, given that the fall time is 100 microseconds (100 μs), we can convert the fall time to seconds by dividing it by 1,000,000. So the fall time in seconds is 100 μs / 1,000,000 = 0.0001 seconds.
Using the formula, we can calculate the charge carried by the lightning stroke during the fall time: Q_fall = I * t = 10,000 A * 0.0001 s = 1 Coulomb.
The total charge carried by the lightning stroke is the sum of the charges during the rise time and fall time: Q_total = Q_rise + Q_fall = 0.1 C + 1 C = 1.1 Coulombs.
Next, let's calculate the peak power of the lightning stroke. Power is defined as the rate at which energy is transferred, and it can be calculated using the formula P = V * I, where P represents power in Watts, V represents potential difference in Volts, and I represents current in Amperes.
Given that the potential difference between the two clouds is 10 million Volts and the peak current is 10,000 Amperes, we can calculate the peak power: P = V * I = 10,000,000 V * 10,000 A = 100,000,000 W or 100 MW (megawatts).
Finally, let's calculate the total energy of the lightning stroke. Energy can be calculated by multiplying power by time. Given that the rise time and fall time are equal, we can use either value.
Using the peak power of 100 MW and the rise (or fall) time of 10 μs (0.00001 seconds), we can calculate the total energy of the lightning stroke: E = P * t = 100,000,000 W * 0.00001 s = 1000 J or 1 kJ (kilojoule).
To summarize:
- The lightning stroke carries a total of 1.1 Coulombs.
- The peak power of the lightning stroke is 100 MW.
- The total energy of the lightning stroke is 1 kJ.