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The current in an RL circuit is zero at time t = 0 and increases to...

The current in an RL circuit is zero at time t = 0 and increases to half its final value in 3 s.

What is the time constant of this circuit?

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Answer #1

For Charging RC circuit, Current is given by:

I = Imax*(1 - exp(-t/T))

T = time constant

Now when I = Imax/2 at . = 3 sec, then

Imax/2 = Imax*(1 - exp(-3/T))

1/2 = 1 - exp(-3/T)

exp(-3/T) = 1/2

-3/T = ln (1/2)

T = -3/ln 0.5

T = time constant = 4.33 sec

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