How long does it take for the current in an RL circuit with R = 150 Omega and L = 67 mH to reach half its fin?

I = V/R(1 - e^(-t/τ)) where τ = L/R

I starts at 0 and rises to a final value of V/R, τ is the time constant

τ = (0.067) /150 = 0.4467 millisecond

V/(2R) = V/R( 1 - e^((-t/τ))

1/2 = 1 - e^(-t/τ)

1/2 = e^(-t/τ)

take the natural log of both sides

ln(1/2) = -t/0.4467

-0.6931 = -t/0.4467

t = 0.3096 milliseconds

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