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anonymous
 5 years ago
The current through a 4F capacitor is given by the equation i(t)=5e^(t/2) for t>0. Assuming that the capacitor is is initially uncharged, determine an expression for the voltage across the capacitor.
anonymous
 5 years ago
The current through a 4F capacitor is given by the equation i(t)=5e^(t/2) for t>0. Assuming that the capacitor is is initially uncharged, determine an expression for the voltage across the capacitor.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i=dq/dt dq=i(dt) integrate to get the charge use charge=capacitance*voltage

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0therefore 4 dv/dt = 5e^(t/2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so \[\frac{dv}{dt} = \frac{5}{4}e^{\frac{t}{2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0integrate both sides with respect to t

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[v = \frac{5}{2}e^{\frac{t}{2}} +C \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, it is initially uncharged, so when t=0, v=0 that gives the constant C = 5/2 \[v(t) = \frac{5}{2} ( 1  e^{\frac{t}{2}}) V \]
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