How long does it take for the current in an RL circuit with R = 150 \Omega and L = 67 mH to reach half its final value?
Answer in ms and explain plz.
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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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