Gerra zemani torrent5/28/2023 The form ofthis solution depends on the roots of the characteristic equation,(1) in which is the damping ratio and is the undamped resonant frequency.The roots of the quadratic equation are equal to,(1b)For the example of the series RLC circuit one has thefollowing characteristic equation for the current i L(t) or v C(t),s 2 + R/L.s + 1/LC =0. Lets focus on the complementary solution. The solution consists of two parts:x(t) = x n(t) + x p(t), in which x n(t) is the complementary solution(=solution of the homogeneous differential equation also called the naturalresponse) and a x p(t) is the particular solution (also calledforced response). Figure 1: Series RLC circuitBy writing KVL one gets a second order differentialequation. ![]() ![]() The discussion is also applicable to other RLC circuits such as theparallel circuit.
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