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anonymous
 one year ago
URGENT!!! RLC Circuit voltage help
anonymous
 one year ago
URGENT!!! RLC Circuit voltage help

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0from \(Q = CV\) for the capacitor, we have \(I = C \dot V\) so \(V(t) = \dfrac{1}{C}\int\limits_{0}^{t} I(t) \; dt \) \( = \dfrac{1}{C}\int\limits_{0}^{t} e^{5t} \; dt \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In your screen capture above, applying Kirchoff's Voltage Law (KVL) around the loop gives \[ v(t)+v _{L}(t) + v _{c}(t) = 0\] where \[v _{L}(t)\] is the voltage across the inductor. Solving gives us: \[v(t) = v _{L}(t)+v _{C}(t)\] Vc(t) is given by the previous responder. \[v _{L}(t) = L \frac{ di _{L} }{ dt }\] where iL is the current through the inductor, but \[i_{L}(t) = i _{R}(t)+i _{C}(t)= \frac{ v _{C}(t) }{ R }+i _{C}(t)\] Since you know \[v _{C}(t), i _{C}(t)\] You can now solve for \[v(t)\]
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