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

AI Thread Summary
The discussion focuses on determining the current in a circuit element based on the charge function q(t)=2(3 − e^{-4t}) for t≥0. The initial attempt at calculating the current resulted in i(t) = 7e^{-4t} + 3, which was incorrect. The correct current is identified as i(t) = 8e^{-4t}. The error was recognized as a simple mistake in the differentiation process. The problem was ultimately resolved by correcting the calculation.
JFonseka
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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?
 
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Nvm. Dumb mistake, just realized. Solved.
 
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