Answer to Question #112500 in Electrical Engineering for Caesar

Question #112500
Problem 1 (5 points). Find the number of electrons as a function of time if: ķ unly 10 Sint → 2pt i(t) = 10 cos(t), to and q(to) = 0
1
Expert's answer
2020-04-28T12:26:42-0400

Our current varies with time according to the law


"i(t)=10\\text{cos}t."

We know that the current is


"i(t)=\\frac{dq(t)}{dt},\\\\\ndq(t)=i(t)dt,\\\\\ndq(t)=10\\text{cos}t\\text{d}t,\\\\\nq(t)=\\int10\\text{cos}t\\text{d}t=10\\text{sin}t+C=10\\text{sin}t"

because "C=q(t_0) = 0."

On the other hand, we know that this charge was produced by electrons charged "e" coulombs each:

"q(t)=N(t)e,\\\\\n\\space\\\\\nN(t)=\\frac{q(t)}{e}=\\frac{10}{e}\\text{sin}t."

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