Final answer:
The total charge passing through a cross-section of the wire in the time interval between t = 0 and t = 8.1 s is found by integrating the current i = 55a - (0.65a/s²)t² with respect to time over the interval.
Step-by-step explanation:
The student is asking about the total charge that passes through a cross-section of a wire in a given time interval when the current varies with time. The provided equation for current is i = 55a - (0.65a/s²)t². To find the total charge (Q) that passes through the wire between t = 0 and t = 8.1 seconds, we need to integrate the current with respect to time.
The charge Q passing through the wire can be calculated using the integral of the current over the given time interval:
Q = ∫ i dt = ∫ (55 - 0.65t²) dt from t = 0 to t = 8.1 s.
Performing this integration yields:
Q = [55t - (0.65/3)t³] from 0 to 8.1
Q = (55 × 8.1) - (0.65/3)(8.1³) coulombs
After calculating this expression, we obtain the total charge in coulombs that passed through the wire in the given time frame.