How Is Current Calculated in a Circuit with Charge Function q(t)?

[JFonseka]

Homework Statement

The total charge that has entered a circuit element is q(t)=2(3 − e$$^{-4t}$$) when t≥0 and
q(t)=0 when t<0. Determine the current in this circuit element for t≥0.

Homework Equations

Differentiation

The Attempt at a Solution

i(t) = 2(4e$$^{-4t}$$) + 3 - e$$^{-4t}$$

i(t) = 7e$$^{-4t}$$ + 3

However the answer says 8e$$^{-4t}$$

What have I done wrong?

 

[JFonseka]

Nvm. Dumb mistake, just realized. Solved.

 

[Moetasim]

Your attempt at a solution is incorrect. The correct solution is:

i(t) = 8e^{-4t}

To find the current, we need to differentiate the given charge function with respect to time. This gives us:

i(t) = d/dt (2(3 − e^{-4t}))

i(t) = 2(d/dt(3) - d/dt(e^{-4t}))

i(t) = 2(0 - (-4e^{-4t}))

i(t) = 8e^{-4t}

Therefore, the current in the circuit element is 8e^{-4t} for t≥0. You may have made a mistake in differentiating the exponential term, which should give -4e^{-4t} instead of 4e^{-4t}. Double check your differentiation steps to find where the error occurred.