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# RLC circuit differential equations

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Using the values L=50*10^-3, R=100 ohms, C= 1600 microF, peak to peak voltage= 200V, and frequency=100Hz, how do I set up and solve the second order differential equation to find the voltage across the capacitance?

I know the equation to use is:

L*(d^2i/dt^2)+R(di/dt)+(1/C)i=wVcoswt

But I am unsure how to solve it to obtain the voltage across the capacitor

Oh, and the intitial conditions are that both the initial voltage across the capacitor and current through the inductor are zero

Edited by NZ

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$L\frac{d^2I}{dt^2}+R\frac{dI}{dt}+\frac{1}{C}=\omega E_0 \cos{(\omega t)}$

try starting with a basic wave equation:

$I_p(t) = A \sin{(\omega t + \phi)}$

differentiate, substitute, and solve . . . .

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Using the values L=50*10^-3, R=100 ohms, C= 1600 microF, peak to peak voltage= 200V, and frequency=100Hz, how do I set up and solve the second order differential equation to find the voltage across the capacitance?

I know the equation to use is:

L*(d^2i/dt^2)+R(di/dt)+(1/C)i=wVcoswt

But I am unsure how to solve it to obtain the voltage across the capacitor

Oh, and the intitial conditions are that both the initial voltage across the capacitor and current through the inductor are zero

Just for something to do I thought I might have a go the "technicians" way.( find Z, Find I, Find Xc etc. backed up by a phasor diag,)

Might be interesting to compare my answer.

To be absolutely clear - you should state in what form you want Vc (presumably V p to p)?

This would be one way to check your answer.

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So what exactly do I solve for?

I assume I go L(-Asin wt) + R(Awcos wt) + (1/C)(Asinwt)=WEo cos wt

But what is the variable I attempt to solve for to find the voltage through the capacitor?

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You have been given everything you need to substitute in proper values, solve for C after finding $\phi$.

Oh you have C, solve for A and $\phi$.

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