The quantity $Q$ of charge in coulombs $C$ that has passed through a point in a wire up to time $t$ (measured in seconds) is given by
$Q ( t ) = t ^ { 3 } - 3 t ^ { 2 } + 4 t + 3$ Find the current when $t = 1 \mathrm {~s}$.
A) 24
B) 15
C) 18
D) 26
E) 1

Question

Quizplus · Accepted Answer

The current $I$ at time $t$ is given by the derivative of the charge $Q(t)$ with respect to time $t$, which is $I(t) = dQ/dt$. For $Q(t) = t^3 - 3t^2 + 4t + 3$, the derivative is $I(t) = 3t^2 - 6t + 4$. Substituting $t = 1$ gives $I(1) = 3(1)^2 - 6(1) + 4 = 3 - 6 + 4 = 1$ A.

The Quantity QQQ Of Charge in Coulombs CCC That Has Passed Through a Point in a Wire Up

The Quantity $Q$ Of Charge in Coulombs $C$ That Has Passed Through a Point in a Wire Up