The switch in the figure is closed at t = 0.Find the time constant of the circui

Question

The switch in the figure is closed at t = 0.Find the time constant of the circuit if L = 24.5 mH, E = 10.5 V, R = 5.43 . Answer in units of ms Calculate the current in the circuit at t = 1.99 ms. Answer in units of A

Explanation / Answer

E-iR=Vl Vl=-Li' =>E-iR=-Li' =>di/dt =-(E-iR)/L =>di/dt= -R/L (E/R -i) =>di/(E/R- i)=-R/L dt =>ln(E/R -i)=-R/L t+c =>i=E/R (1-A e^(-R/Lt)) at t=0 i=0 =>A=1 =>i=E/R(1-e^(-R/L t)) time constant =L/R= 24.5*10^-3/5.43 = 4.512 ms i=E/R (1- e^(-R/Lt)) i=10.5/5.43 (1-e^(-221.63t)) i(t=1.99ms)=1.934 *(1-e^(-221.63*1.99*10^-3))=.689733A

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