Answer:
The current at t = 0 is
[tex]I (0) = 2[/tex] units of current
Step-by-step explanation:
If the current flowing through an electric circuit is defined as the derivative of the charge as a function of time and we have the equation of the charge as a function of time, then, to find the equation of the current, we derive the equation of the charge.
[tex]q (t) = 3t ^ 2 + 2t-5[/tex]
[tex]\frac{dq(t)}{dt} = 3 (2) t ^ {2-1} +2t ^ {1-1} -0[/tex]
Simplifying the expression we have:
[tex]\frac{dq(t)}{dt} = 6t + 2t ^0\\\\\frac{dq(t)}{dt} = 6t + 2 = I (t)[/tex]
Finally, the equation that defines the current of this circuit as a function of time is:
[tex]I (t) = 6t +2[/tex]
Now to find the current at t = 0 we make [tex]I (t = 0)[/tex]
[tex]I (0) = 6 * 0 +2[/tex]
[tex]I (0) = 2[/tex] units of current
