Question

(1 point) A resistor R=30 N is in series with an inductor L = 2.2 mH and a 70 V battery. The switch is closed at t = 0. At what time will the power loss in R equal the rate at which energy is being stored in L? ms

Answer 1

R=302 L=2.2 MH i1t) t=0 ot Tov. Current i (0) + [ilo)- íloo)] et/z. when switch is closed at t=0 the througe R,L will start increasing The egn. of current ilt) is given by -t/z. ilt) = 2100) [at at to L act as Short circuit {(o)= 0 [i nothing is given about initial Condition]. -tel ilt) ,2 TO. 7 30 3 / ZAL R

→ since current is increasing, in the inductor will increasing the energy increase gradually. inductor is given by Energy af E = ist² E 2 in resistor ilt) R. Energy dissipated Alq question, dll R List 2 = 1 (+)² dt 7 to 2. ilt) 2. lL ilt) dilt) 2. 2 at ilt). R di at it) en [11-4)= (-7 %) R IN

- the 7 e 311-28). [: By -t/2 -t/7 1 - e е >) -t/z 2 e c 1 - -005 7 luo.s t 0.6931 >> t = 0.69 37% z 3 V t = 0.6931.8 2.2x10 30 t = 0.05 ms. itt) wite t