if you can explain in detail ill reall appreciate many thanks in advance An emf

Question

if you can explain in detail ill reall appreciate many thanks in advance

An emf of 10V is connected to the RL circuit (R = 10 Ohms. L = 1.0 H) shown below for long, long time (the switch is in position 1). Then, at t = 0 the switch is thrown into position 2. Find the current in the circuit at t = 0.2 s. When will the current drop to 0.001 A?

Explanation / Answer

at t=0.2 s--->tau=L/R=1/10=0.1 s--->V/R*(1-e^(-10*0.2))=8.65 A i forced=V/R--->i natural=-Io*e^(R/L*t) iL(t)=V/R*[1-e^(-R/L*t)]:0.001=V/R*[1-e^(-10*t)] V/R=1 A forced--->-1 A*e^(-10*t) A natural--->0.001=1-1*e^(-10*t) (0.001-1)=-e^(-10*t)--->Ln((0.001-1)/-10=t=0.00010005 s at t=0.2:8.65 A at A=0.001:t=100.05 micro s

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