Question
The current in a wire varies with time according to the relationship $I = 55 A$ - $10.65 A/s{^2}2t{^2}$. (a) How many coulombs of charge pass a cross section of the wire in the time interval between $t =$ 0 and $t =$ 8.0 s? (b) What constant current would transport the same charge in the same time interval?
Step 1
The current is given by the equation $I = 55 A - 10.65 A/s^2 t^2$. We want to find the total charge from $t = 0$ to $t = 8.0 s$, so we integrate the current from 0 to 8.0 s: $$Q = \int_{0}^{8.0} I dt = \int_{0}^{8.0} (55 - 10.65t^2) dt$$ Show more…
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