Question

URGENT!!! RLC Circuit voltage help

Answer 1

from \(Q = CV\) for the capacitor, we have \(I = C \dot V\)
so \(V(t) = \dfrac{1}{C}\int\limits_{0}^{t} I(t) \; dt \)

\( = \dfrac{1}{C}\int\limits_{0}^{t} e^{-5t} \; dt \)

Answer 2

In 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 \[v(t)\]