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A battery with emf is connected in series with an inductance L and a resistance R. Assuming the current has reached steady state when it is at 99% of its maximum value, how long does it take to reach steady state, assuming the initial current is zero? (Use any variable or symbol stated above as necessary. To represent e m f, use E.)

Answer :

Answer: t=4.6*R*L

Explanation: In order to explain this problem we have to take into account the expression for the current in a RL electric circuit, which is given by:

[tex]i(t)=if*(1-^{-t/R*L})[/tex]

where If is the final current for RL circuit If (emf/R)

Considering the final current is getting when I(t) = 0.99*If we have:

[tex]0.99*if=if*(1-^{-t/R*L})[/tex]

reoganising the terms we have:

e^(-t/R*L)=(1-0.99)

ln(e^(-t/R*L))=ln(0.01)

then t=4.6*R*L

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