Weget d 2i t r di t 1 1 dvs t i t 2 dt l dt lc l

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Unformatted text preview: d the inductors are replaced by short circuits. This leads to the circuit being reduced to a purely resistive circuit and hence can be analyzed using earlier mentioned methods. RL circuits The method of finding the current and voltage is similar to the method used for RC circuits. t 0 iL (t ) vL (t ) Steps: 1. Apply Kirchoff’s current and voltage laws to write the circuit equation. Vs RiL L diL dt 2. Rearrange the equation to obtain a first order differential equation with the inductor current as the variable of interest. L diL RiL Vs dt 3. Assume a solution of the form iL (t ) K1 K 2 e st . LK 2 se st R ( K1 K 2 e st ) Vs RK1 K 2 ( Ls R )e st Vs 4. Substitute the solution into the differential equation to determine the value of K1 and s . Vs R R Ls R 0 s L RK1 Vs K1 5. Use the initial conditions to determine the value of K 2 . As the inductor current cannot change instantaneously, iL (t 0) 0 0 Vs V K2 K2 s R R 73 EE1002 Introduction to Circuits and Systems 6. Write the final solution. VS VS R t eL RR L Here is...
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This document was uploaded on 01/20/2014.

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