Laplace transforms:Series RLC circuit

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Laplace Transform Example: Series RLC Circuit

Problem

Given a series RLC circuit with Failed to parse (syntax error): {\displaystyle R=10 Ω} , , and , having power source , find an expression for if and .

Solution

We begin with the general formula for voltage drops around the circuit:

Substituting numbers, we get

Now, we take the Laplace Transform and get

Using the fact that , we get

Using partial fraction decomposition, we find that

<math>\Rightarrow I(s)=\dfrac{6.24*10^7-s}{4.98*10^6s^2+1.25*10^7s+1.25*10^{12}}+\dfrac{