Problem 1 - Physics

Question

A lightning bolt delivers a charge of \(35 \mathrm{C}\) to the ground in a time of \(1.0 \times 10^{-3} \mathrm{~s}\). What is the current?

Step-by-Step Solution

Answer

The current is 35,000 A.

Step 1: Understanding the Problem

The problem involves calculating the current when the charge and time are given. The charge delivered is given as 35 C (coulombs) and the time over which this charge is delivered is given as \(1.0 \times 10^{-3} \mathrm{~s}\). We need to find the current (I).

Step 2: Applying the Formula for Current

Current \(I\) can be calculated using the formula \(I = \frac{Q}{t}\), where \(Q\) is the charge and \(t\) is the time. Here, \(Q = 35\) C and \(t = 1.0 \times 10^{-3}\) s.

Step 3: Substituting Values

Substitute the values of \(Q\) and \(t\) into the formula: \[I = \frac{35 \mathrm{~C}}{1.0 \times 10^{-3}\mathrm{~s}}\].

Step 4: Calculating the Current

Perform the calculation to get \[I = 35 \times 10^3 \mathrm{~A}\]. This equals \(35,000 \mathrm{~A}\).

Step 5: Conclusion

The current delivered by the lightning bolt is 35,000 A (amperes).

Key Concepts

Charge

In the realm of electric circuits, the concept of **charge** is pivotal. It relates to the property of particles which enables them to exert electric forces on each other. Charged particles are the foundation of electricity.

• **Charge** is measured in units called **coulombs (C)**.
• It's essential to know that one coulomb is a substantial amount of charge, which pertains to about 6.242 x 10^18 electrons.

When you look at a problem statement describing a lightning bolt delivering a charge of 35 C to the ground, it refers to a vast quantity of electrons being transferred. In these exercises, it's crucial to consider the direction of charge flow. Positive charge flows from the positive terminal to the negative, simulating the natural flow of positive ions.

Time

Understanding the **time** element is crucial in measuring electric current. It dictates the duration over which a specific amount of charge is moved.

• Time is typically measured in **seconds (s)** in the context of electricity.
• The shorter the time for a given charge to move, the higher the current.

In the given lightning bolt example, the charge moves in an exceptionally short time of 1.0 x 10^{-3} s, which is equivalent to a millisecond. This demonstrates that when such a vast amount of charge moves almost instantaneously, the resulting current is significant.

Amperes

The term **amperes** (A) is the unit of measurement for electric current. Current is defined as the rate of flow of charge through a surface. Calculating the current involves the relationship between charge and time:

• Expressed through the formula: \[ I = \frac{Q}{t} \]
• Where \( I \) is the current in amperes, \( Q \) is the charge in coulombs, and \( t \) is the time in seconds.

In the exercise, substituting 35 C for charge and 1.0 x 10^{-3} s for time into the formula yields a current of 35,000 A. This colossal current value indicates the immense power delivered by a lightning bolt in such a short span. This comprehension of current and amperes is fundamental for both scientific and practical applications in understanding electric phenomena.