NZ Posted March 26, 2012 Posted March 26, 2012 (edited) 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 March 26, 2012 by NZ
Xittenn Posted March 26, 2012 Posted March 26, 2012 [math] L\frac{d^2I}{dt^2}+R\frac{dI}{dt}+\frac{1}{C}=\omega E_0 \cos{(\omega t)}[/math] try starting with a basic wave equation: [math] I_p(t) = A \sin{(\omega t + \phi)} [/math] differentiate, substitute, and solve . . . .
Joatmon Posted March 26, 2012 Posted March 26, 2012 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.
NZ Posted March 26, 2012 Author Posted March 26, 2012 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?
Xittenn Posted March 26, 2012 Posted March 26, 2012 You have been given everything you need to substitute in proper values, solve for C after finding [math] \phi [/math]. Oh you have C, solve for A and [math] \phi [/math].
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