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So I need to find the current labeled as a function of time. THe switch opens at t=0 and I drew the circuit after the switch opens.

I found the initial current to be -4 and the voltage on the capacitor to be 8.

I'm having trouble trying to find [itex]di_L(0)/dt[/itex]. I know you just need to do a simple loop around the whole circuit, [itex]v_c+v_l+v_r=0[/itex]. The problem is I don't know the signs of the voltages, or rather I don't know what they should be. I get either [itex]di_L(0)/dt = -40/10, -24/10[/itex].

Same for finding the second order eq.

[itex]1/c\int i_c+ L di_L/dt + 8 i_L = 0[/itex] Simple loop around the outside. Are signs correct?

and

[itex]i_c - i_L - V_2/2 = 0[/itex] Node equation at the top node, V is equal to the voltage across the inductor and 8 ohm resistor so substitute

[itex] i_c - i_L - 1/2 (Ldi_L/dt + 8i_L)=0[/itex]

Substitute the third into the first, do algebra, and find answer.

That part should be easy. What I need to know is whether the signs are correct. That is, when doing kichoff mesh and nodes how do you know what is positive and negative [or rather what side the element should be placed on]?

Thanks

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# Homework Help: Second order RLC circuit

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