using the laplace transforms, find the charge and the current in a series LRC circuit where L = 1/2 h R = 10 ohms C = 1/30 f E(t) = 300V q(0) = 0 C i(0) = 0 A
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Step 1: Start with the differential equation for the series LRC circuit: \[ L\frac{d^2q}{dt^2} + R\frac{dq}{dt} + \frac{q}{C} = E(t) \] Show more…
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Recall that the differential equation for the instantaneous charge $q(t)$ on the capacitor in an $L R C$ -series circuit is $$ L \frac{d^{2} q}{d t^{2}}+R \frac{d q}{d t}+\frac{1}{C} q=E(t) $$ See Section 3.8. Use the Laplace transform to find $q(t)$ when $L=1 \mathrm{~h}, R=20 \Omega, C=0.005 \mathrm{f}, E(t)=150 \mathrm{~V}, t>0, q(0)=0$ and $i(0)=0$. What is the current $i(t) ?$
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