Question

A thundercloud similar to the one described in Example 24.3 produces a lightning bolt that strikes a radio tower, If the lightning bolt transfers \(5.00 \mathrm{C}\) of charge in about \(0.100 \mathrm{~ms}\) and the potential remains constant at \(70.0 \mathrm{MV}\), find (a) the average current, (b) the average power, (c) the total energy, and (d) the effective resistance of the air during the lightning strike.

Short answer

Question: A lightning strike transfers a charge of 5.00 Coulombs in 0.100 milliseconds through a potential difference of 70.0 Megavolts. Calculate the average current, average power, total energy, and effective resistance of the air during the lightning strike. Solution: Step 1: Calculate the average current: I = Q / t I = (5.00 C) / (0.100 ms) = 5.00 C / 0.000100 s I = 50,000 A (Amperes) Step 2: Calculate the average power: P = V × I P = (70.0 MV) × (50,000 A) P = 3,500,000,000,000 W (Watts) or 3.50 TW (Terawatts) Step 3: Calculate the total energy: E = V × Q E = (70.0 MV) × (5.00 C) E = 350,000,000 J (Joules) Step 4: Calculate the effective resistance: R = V / I R = (70.0 MV) / (50,000 A) R = 1,400 Ω (Ohms) The average current is 50,000 A, the average power is 3.50 TW, the total energy is 350,000,000 J, and the effective resistance of the air during the lightning strike is 1,400 Ω.

Step-by-step solution

Calculate the average current

To find the average current, divide the total charge by the time it took for the charge to transfer. Use the formula: I = Q / t I = (5.00 C) / (0.100 ms) = 5.00 C / 0.000100 s

Calculate the average power

To find the average power, multiply the potential difference by the average current. Use the formula: P = V × I P = (70.0 MV) × (5.00 C / 0.000100 s)

Calculate the total energy

To find the total energy, multiply the potential difference by the total charge. Use the formula: E = V × Q E = (70.0 MV) × (5.00 C)

Calculate the effective resistance

To find the effective resistance, divide the potential difference by the average current. Use the formula: R = V / I R = (70.0 MV) / (5.00 C / 0.000100 s) After completing these steps, you'll have the average current, average power, total energy, and effective resistance of the air during the lightning strike.