NZ 10 Posted March 26, 2012 Share 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 Link to post Share on other sites

Xittenn 176 Posted March 26, 2012 Share 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 . . . . Link to post Share on other sites

Joatmon 108 Posted March 26, 2012 Share 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. Link to post Share on other sites

NZ 10 Posted March 26, 2012 Author Share 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? Link to post Share on other sites

Xittenn 176 Posted March 26, 2012 Share 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]. Link to post Share on other sites

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