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The current in a wire varies with time according to the relation i = 55a - (0.65a/s²)t². How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and t = 8.1 s?

User Maddison
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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.

User Chris Stryker
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