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5) Let vc(t) across the capacitor; R the resistance; C the capacitance, and V(t) the voltage supplied by the voltage source. See the figure below. dvc We get RC +vc...

Question

5) Let vc(t) across the capacitor; R the resistance; C the capacitance, and V(t) the voltage supplied by the voltage source. See the figure below. dvc We get RC +vc = Vt) dt R 20 4v F Suppose the voltage source, V(t) = 4 and the Initial voltage across the capacitor vc(0) = 6 With quantities R = 2 and C = 1 we get the Initial value problem. dvc 2 +Vc =4 dt Vc(0) = 6 (Note: These numbers are probably unrealistic. However; we want to get the idea of how to solve these types of problems) Find the vo

5) Let vc(t) across the capacitor; R the resistance; C the capacitance, and V(t) the voltage supplied by the voltage source. See the figure below. dvc We get RC +vc = Vt) dt R 20 4v F Suppose the voltage source, V(t) = 4 and the Initial voltage across the capacitor vc(0) = 6 With quantities R = 2 and C = 1 we get the Initial value problem. dvc 2 +Vc =4 dt Vc(0) = 6 (Note: These numbers are probably unrealistic. However; we want to get the idea of how to solve these types of problems) Find the voltage across the capacitor, Vc(t) using Laplace transforms



Answers

IMI The circuit in the figure is described by the equation
$$
\left[\begin{array}{c}{i_{L}^{\prime}} \\ {v_{c}^{\prime}}\end{array}\right]=\left[\begin{array}{cc}{0} & {1 / L} \\ {-1 / C} & {-1 /(R C)}\end{array}\right]\left[\begin{array}{c}{i_{L}} \\ {v_{c}}\end{array}\right]
$$
where $i_{L}$ is the current through the inductor $L$ and $v_{C}$ is the voltage drop across the capacitor $C .$ Find formulas for $i_{L}$ and $v_{C}$ when $R=.5$ ohm, $C=2.5$ farads, $L=.5$ henry,
the initial current is 0 amp, and the initial voltage is 12 volts.


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