Question

gmor reaion tlr am in condition(20) 2. For the following circuit, write the differential equation for iR, the current through the resistor, Boundary conditions are not needed. R-100hms, C-1F, L=1mH (20). L C in out 1R

Answer 1

"d^2 v/dx^2 + 2 dv/dx + 20 v = 0 md^2 v/dx^2 + b dv/dx + kv = 0 form above equation we find = b^2 - 4ac = 0 b = 2 a = 1 c = 20 b^2 = 4 4ac = 4 times 1 times 20 = 80 b^2 < 4ac we know b^2 < 4 mk under damping b^2 > 4 mk over damping b^2 = 4 mk critical damping d^2 v/dx^2 + 2dv/dx + 20v = 0 b^2 < 4 mk under damping condition \r\n Apply KVL V_L + V_c + V_R = 0 L di/dt + 1/c integral I dt + iR = 0 differentiating with respect to ""t"" L d^2i/dt^2 + 1/ci + di/dt R = 0 L d^2i/dt^2 + di/dt R + 1/ci = 0 l times d^2i/dt^2 + 100 di/dt + 1/c = 0 d^2i/dt^2 + 100 di/dt + 1/c = 0"

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