0 overdamped 1 critically damped 1 and under damped

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Unformatted text preview: the time constant of the RL circuit similar to the RC circuit. R iL (t ) The value of the inductor current after time equal to the time constant would be 0.632 times its steady‐state value. After 5 times the time constant, the inductor current will be almost equal to the steady‐state current. RC and RL circuits with general sources Solution of the Differential Equation The general differential equation of a circuit containing resistance and inductance or capacitance is: dx(t ) x(t ) f (t ) . dt The general solution to this will consist of two parts: 1. The first part is called a particular solution or forced response because it depends on the forcing function. 2. The second part is called the complementary solution and is the solution of the homogenous equation viz. dxc (t ) xc (t ) 0 . dt The particular solution satisfies the differential equation, but it may not be consistent with the initial conditions. By adding the complementary solution, the general solution satisfies both the differential equation and the initial conditions. The particular solution is o...
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This document was uploaded on 01/20/2014.

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