Question

The total amount of electric charge that has passed through a particular wire is given as a function of time by q=14e-ᵗ/⁸

, where q is the amount of charge in coulombs and t is the time in seconds. Find the current, in units of coulombs per second, flowing through the wire at time t=7. Round your answer to two decimal places.

Answer 1

The current flowing through the wire at time t=7 is approximately -0.39 coulombs per second.

Step-by-step explanation:

To find the current flowing through the wire at a specific time, we need to differentiate the charge function q(t).

Given q(t) = 14e^(-t/8), we can differentiate it with respect to time t to find the current function i(t).

i(t) = d(q(t))/dt = d(14e^(-t/8))/dt = -14e^(-t/8)/8

Plugging in t = 7 into i(t), we get i(7) = -14e^(-7/8)/8. Rounding this answer to two decimal places, the current flowing through the wire at time t=7 is approximately -0.39 coulombs per second.