Answer to Question #264258 in Electric Circuits for Rex

Question #264258

Determine the current flowing through an element if the charge flow is given by a. q(t)= (3e^-t -5e-^2t) nC b. q(t)= 10sin120πt pC c. q(t)= 20e^-4t cos50t µC

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Expert's answer
2021-11-17T10:42:26-0500

(a) The current can be found as


I=dq/dt, I=ddt(3et5e2t)=e2t(103et) nA.I=\text dq/\text d t,\\\space\\ I=\frac{\text d}{\text d t}(3e^{-t} -5e^{-2t})=e^{-2t}(10-3e^t)\text{ nA}.

(b) The current is


I=dq/dt, I=ddt[10sin(120πt)]=1200πcos(120πt) pA.I=\text dq/\text d t,\\\space\\ I=\frac{\text d}{\text d t}[10\sin(120πt)]=1200\pi\cos(120\pi t)\text{ pA}.

(c) The current:


I=ddt[20e4tcos(50t)]= =40e4t[25sin(50t)+2cos(50t)] μA.I=\frac{\text d}{\text d t}\Big[20e^{-4t}·\cos(50t)\Big]=\\\space\\ =-40e^{-4t}[25\sin(50t)+2\cos(50 t)]\space\mu\text{A}.


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