ODE's/Elec Eng'g: The circuit elements in a strictly parallel RLC circuit are R = 312.5 Ohms, L = 50 mH, and C = 200 nF. The initial inductor current is -45 mA, and the initial capacitor voltage is 15V. Find v(t) for t>=0, where t is in milliseconds. (Illustration attached in the first comment)
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This was my solution, but the homework console doesn't seem to accept this as the right answer: http://www.wolframalpha.com/input/?i=v%27%27+%2B+%281%2F%28312.5*200E-9%29%29v%27+%2B+%281%2F%2850E-3+*+200E-9%29%29v+%3D+0%2C+v%280%29+%3D+15%2C+v%27%280%29+%3D+-15
Since the problem didn't give v'(0) directly, I solved for v'(0) first by using the equation i_C(0) = C dv(0)/dt. By Kirchoff's current law, -i_C(0) - i_R(0) - i_L(0) = 0. i_R(0) is just v_C(0)/R which is 15V/312.5 Ohms = 0.048 A. i_L(0) is given in the problem, which is -45 mA. Thus i_C(0) = 0.048 A - .045 A = .003 A. Thus, dv(0)/dt = i_C(0)/C = (.003 A)/(200E-9 F) = 15000 V/s. Since the problem is asking for t in ms, I used v'(0) = 15 V/ms. Still, this didn't work though.