Question

Find ic(t) in the circuit below for t30. (25 points) t=0 5xic swi R1 50 V3 SV icle

Answer 1

closed switch Ps 1 the initially capacitor closed and capacitor through the resistor (R) Q. When the switch is not is unchanged. At +=0 Starts charging where g(t) = charge capacitor at time t and cusent in CRT at time to oh R,=52 S mm int G 21+) V = sport Apply KVL at bop Supao sum -V₂ + ict) R, i(+1R, + 2(+) Vz (a la The C=YNF с. PHIR 2(+) co i(t) ㅗ Q(+) RC dq Current in is CKT given by ilt) dt 02 < (GV3 - 264) ) dt RG de dt Quq RICO Prlegrate Both sides .q dQ at (as at time to CV-2 RCI Capacitor es unchanged T=0 9=0 os 2(t+o) 30 ) (4-0) In (CN-2) RIC, -1 900 thwest f

in In CV₃ - 2 -+ RG c GV₂-0 -TRG e (Na-2 GV₃ -t/Rico I-2 e GV₃ I alla -t/Roca -t/RCO - i-e ☆ 9(+) = CV3 (i-e Ps -TIRICI The cuvent through CKT prt) d2 dt ist e EN & li-e dt -AIRCO ARICO CVS CO ella Comments RCI -t/Rico i(t) = e where time constant Ri で RG T = sx4x100 = 20 Hsec so cusent at time t -te itt) 1.0 e And 5 es RI S The some current flows through the capacitor at time t -te ( (t) = 1.0 e App where "С = 20 Msec I ARO