Question

ENS 233 O Giver he vellese and current or the following circuit -5t fahd e ofind the sneru stored on he Gisen the Lolbsing nehoork, determine the 70 rindeypressons-for-ce(t) and e(4) n the 241

Answer 1

KVL - V(t) + i(t) R = 0 8e^-5t + 20 mu A e^-5t R = 0 20 times 10^-6 e^-5t R = 8e^-5t R = 8/20 times 0 = 0.4 times 10^6 ohm V(t) = 8e^-5t v(t) = 20 mu A e^-5t R = 0.4 times 10^6 ohm R = 400 k ohm Applying KCL i_C(t) = -i(t) = -20 mu A e^-5t for capacitor i_c(t) = C middot dv_C/dt -20 mu Ae^-5t = C times d/dt 8e^-5t d/dt e^-at = -ae^-at -20 times 10^-6 e^-5t = C times 8 times (-5)e^-5t -20/-40 1/2 times 10^-6 = C C = -0.5 mu F C) Energy stored an the capacitor at t = 0 is E = 1/2CV^2(0) V(0) = 8e^-5(0) e^0 = 1 = 8 E = 1/2 times 0.5 times 10^-6 times 8^2 E = 16 mu J \r\n for t proportionalto 0 circuit will be Assuming circuit is at t = 0^- form -infinity time