Question

During lightning strikes from a cloud to the ground, currents as high as 25,000 A can occur and last for about 40 ms. How much charge is transferred from the cloud to the earth during such a strike?

Short answer

1,000 Coulombs of charge is transferred.

Step-by-step solution

Understand the Problem

The problem involves calculating the amount of electric charge transferred during a lightning strike. The lightning current is given as 25,000 A and it lasts for 40 ms (milliseconds). We will use the formula for electric charge, which is the product of current and time.

Convert Time to Seconds

The time given is in milliseconds (ms). To use in the formula, convert it to seconds. Since 1 second = 1000 milliseconds, 40 ms = 40/1000 = 0.04 seconds.

Use the Formula for Charge

The formula to calculate the electric charge transferred is:\[ Q = I imes t \]where \( Q \) is the charge (in Coulombs), \( I \) is the current (in Amperes), and \( t \) is the time (in seconds). Substitute the known values: \( I = 25,000 \, A \) and \( t = 0.04 \, seconds \).

Calculate the Charge

Substitute the values into the formula:\[ Q = 25,000 \, A imes 0.04 \, s = 1,000 \, C \]So, the charge transferred during the lightning strike is 1,000 Coulombs.

Key concepts

Understanding Lightning Strike Current

Lightning is an impressive natural phenomenon and involves enormous electric currents. When lightning strikes, it results from a rapid discharge of electric charge accumulated in the clouds. The current in a lightning strike can reach extremely high values, typically ranging from thousands to tens of thousands of Amperes, like the 25,000 Amperes mentioned in the exercise.

This high current is the result of the massive buildup of electric charge in the cloud and its sudden release during a strike. This discharge causes the current to spike and, despite lasting only a brief moment, it is powerful and can transfer a significant amount of electric charge. Knowing the current helps in understanding how much electric power is being transferred from the cloud to the ground, which is a crucial factor in calculating the electric charge transferred.

Exploring the Electric Charge Formula

Electric charge is a fundamental property of matter and is measured in Coulombs (C). To calculate the amount of electric charge transferred in any process, you use the formula:

• \[ Q = I \times t \]

where:

• \( Q \) is the electric charge in Coulombs,
• \( I \) is the current in Amperes,
• \( t \) is the time in seconds.

This formula is based on the relationship that charge is equal to the product of current (flow of electric charge) and the time the current flows.

Essentially, if you have a steady flow of current that lasts for a particular duration, this formula gives you the total electric charge transferred during that time period. For instance, if a 25,000 Ampere current flows for 0.04 seconds, the charge transferred is \( 25,000 \times 0.04 = 1,000 \) Coulombs.

Converting Time to Seconds

Understanding time conversion is crucial when working with formulas as they often require consistent units. In the context of the exercise, the duration of the lightning strike is given in milliseconds (ms), a unit often used to measure very brief periods of time. However, to use this duration in the electric charge formula, we need to convert it to seconds.

The conversion is straightforward.

• Since 1 second equals 1,000 milliseconds, the time conversion is simply dividing the milliseconds by 1,000.
• For instance, 40 milliseconds becomes \( 40/1000 = 0.04 \) seconds.

By ensuring we convert any given time into seconds, we maintain consistency and accuracy in calculations involving electric charge, making it easier to apply formulas correctly and arrive at the right solution.