Question

his circuit, att othe switch is slammed into position A, causing the current through the 5 seconds the switch is sammed into inductor to increase from pro to some val position B, causing the current through the inductor to decrease from this value. eventualni to zero. Answer these questions: Find the current when t-5 b. Find the current 4. For this circuit, switch thrown ett. Find: a. The equation for the current through the inductor for the current through the swtch

I'm almost done with this problem, part a answer is circled but part b I can't remember how to integrate something like this. please help, calculus involved physics, thank you!

Answer 1

I hope the values of resistances & inductors are currect as they aren't clear from the diagrams. from t 0 to t 5s, loop I is activated by the switch. I Io(1 - e^-t/tau) E/R(1 - e-t/tau) 10/2(1-e^-t/3) I(t 5) 5(1 - e^-5/3) I(t 5) 4.056A Now from t 5s to t 10s loop gets activated as the switch position is changed. Using KVL, -Ldi/dt - Reqi 0 integral di/dt integral - Reqi/L integral ii if di/i -(Req/L) integral 0 t dt ln if/ii -(Req/L)t if ii e^-t/tau^1 if 4.056 e^-5/1 if 0.0273A