To tackle this problem, we need to analyze the current flowing through the wire over a specified time interval and then determine the total charge that passes through a cross-section of the wire. Let's break it down step by step.

Understanding Current and Charge

Current (I) is defined as the rate of flow of electric charge. Mathematically, it can be expressed as:

I = dQ/dt

Where dQ is the differential charge and dt is the differential time. To find the total charge (Q) that flows through the wire over a time interval, we can integrate the current over that time period:

Q = ∫ I(t) dt

Part A: Calculating Total Charge

Assuming the current varies with time according to a specific function I(t), we need to integrate this function from t = 0 to t = 8 seconds. Let's say the function is given, and we find that:

Q = ∫ I(t) dt from 0 to 8

If the result of this integration gives us Q = 330 C, it means that 330 coulombs of charge pass through the cross-section of the wire during this time interval.

Part B: Finding Constant Current

Next, we need to determine what constant current would transport the same amount of charge (330 C) in the same time interval (8 seconds). The formula for current can be rearranged to find a constant current (I_constant):

I_constant = Q / t

Substituting the values we have:

I_constant = 330 C / 8 s = 41.25 A

For practical purposes, we can round this to 41 A. This means that a constant current of 41 A would transport the same charge of 330 C in 8 seconds.

Summary of Results

• Total charge passing through the wire: 330 C
• Equivalent constant current: 41 A

This analysis illustrates the relationship between current, charge, and time, highlighting how varying current can be integrated to find total charge and how a constant current can be calculated to match that charge over a specific time frame.