For the following characteristic equations, write corresponding differential equ

Question

For the following characteristic equations, write corresponding differential equations and final all roots, whether real, imaginary, or complex: 4s + 9 = 0, 2s - 4 = 0; s2 + 7s + 1 = 0; 5s2 + 8s + 18 = 0. 7. With the assumption that the switch in the circuit of Fig. 8.54 has been closed a long, long, long time, calculate iL(t) at (a) the instant just before the switch opens; the instant just after the switch opens; t = 15.8 mu s; t = 31.5 mu s; t = 78.8 mu s. The switch in Fig. 8.54 has been closed since Catfish Hunter last pitched for the New York Yankees. Calculate the voltage labeled v as well as the energy stored in the inductor at (a) the instant just prior to the switch being thrown

Explanation / Answer

switch closed, inductor acts as short circuit, so il(0-)= 4mA as inductor opposes any sudden change in current, so il(0+)= 4mA R/L= 220/2m = 0.11s il(t)= 4mA (e^-Rt/L) il(t=15.8us) = 3.999 mA il(t=31.5us)= 3.998 mA il(t=78.8us) = 3.997mA

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