The current in a wire varies with time according to the...

The current in a wire varies with time according to the relationship $I=55 \mathrm{~A}-\left(0.65 \mathrm{~A} / \mathrm{s}^{2}\right) t^{2} .$ (a) How many coulombs of charge pass a cross section of the wire in the time interval between $t=0$ and $t=8.0 \mathrm{~s} ?(\mathrm{~b}) \mathrm{What}$ constant current would transport the same charge in the same time interval?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Antiderivatives in Calculus

Antiderivatives are used to compute integrals, which is essential for determining the cumulative effect of a time-varying quantity. In the context of electric circuits, applying the antiderivative to the function describing current as a function of time provides a method to find the total charge delivered over a specified period.

Time Integration of Current

This concept involves calculating the total charge that passes through a point by integrating the time-dependent current over the given time interval. In cases where the current is not constant, the integration yields the area under the current-versus-time curve, representing the cumulative electric charge transported.

Average Current

The average current is defined as the total charge transferred divided by the total time interval during which the transfer occurs. For a variable current, determining a single equivalent constant current that delivers the same total charge requires calculation of this average value, ensuring that Q = I_avg × time.

Transcript

Please give Ace some feedback