- #1

jaus tail

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- 48

## Homework Statement

Initially switch is at 0.

At t = 0 seconds switch is put at 1.

After 1 time constant switch is put at 2.

Find equation for current for t > 2[/B]

## Homework Equations

current through inductor tries to remain constant.

i(t) through inductor in series RL circuit is i(t) = [ i(initial) - i(final) ] e

^{(-R*t/L}+ i(final)

## The Attempt at a Solution

At t < 0 I(t) is 0.

For t > 0 switch is in position 1.

i(t = 0

^{+}) = i(t = 0

^{-}) = 0.

for t much more than 0, the inductor will be short circuit and i will be 100 volts / 1 ohm = 100 A.

so equation for t > 0 = (initial current - final current) e

^{-R*t/L}+ final current

= (0 - 100)e

^{(-1 * t / 1}+ 100 = 100 (1 - e

^{(-t)})

Now at t = 1 time constant switch is at position 2.

time constant = L/R = 1/1 = 1 second.

At t = 1 second, i(t) = 100 (1 - e

^{-1})

= 63A

Now at t = 1 second switch is at position 2.

So initial current is same as earlier which is 63A.

Final current is 50A.

So we get answer as [ initial - final ] e

^{(-t)}+ final

which is (63 - 50 ) e

^{-t}+ 50

= 50 + 13e

^{(-t)}

But in answer they've given

50 + 13e

^{-(t-1)}

Where did the -1 part come from?