Engineering, 04.01.2020 01:31 memester74
There is no charge at the upper terminal of the ele- ment in fig. 1.5 for t 6 0. at t = 0 a current of 125e-2500t ma enters the upper terminal. a) derive the expression for the charge that accu- mulates at the upper terminal for t 7 0. b) find the total charge that accumulates at the upper terminal. c) if the current is stopped at t = 0.5 ms, how much charge has accumulated at the upper terminal?
Answers: 1
![q(t)=50[1-e^{-2500t}]\mu C](/tpl/images/0441/9010/1f7f8.png)
![q(t)=\int\limits^t_0 {I(t)} \, dt\\q(t)=\int\limits^t_0 {125e^{-2500t} mA} \, dt\\q(t)=(125\times 10^{-3})[\frac{e^{-2500t}}{-2500}]^{t}_{0}\\\\q(t)=( 50\times 10^{-6})[-e^{-2500t}]^{t}_{0}\\\\q(t)=( 50\times 10^{-6})[-e^{-2500t}+1]\\\\](/tpl/images/0441/9010/3360e.png)
![q(t)=50[1-e^{-2500t}]\mu C---(1)](/tpl/images/0441/9010/8e0f7.png)
![q(t)=( 50\times 10^{-6})[1-e^{-2500(\infty)}]\\q(t)=(50\times 10^{-6})[1-0]\\q(t) =50\mu C](/tpl/images/0441/9010/c8288.png)
![q(t)=( 50\times 10^{-6})[1-e^{-2500(0.5\times10^{-3})}]\\q(0.5ms)=35.67\mu C](/tpl/images/0441/9010/84e8a.png)
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There is no charge at the upper terminal of the ele- ment in fig. 1.5 for t 6 0. at t = 0 a current...
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