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sugz
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Homework Statement
For the circuit in the attached file, find io (current) for t>0
Homework Equations
The Attempt at a Solution
I have included an attachment which shows the solution. However, I will copy the solution here as well for reference:
When t<0, the switch is closed, the inductor acts as a short circuit to dc. The question I have in this step is what happens to the resistor that is in series with the inductor when the inductor becomes a short circuit?
The resulting circuit is one with the 24V source, 4 ohm resistor and the 4 ohm and 8 ohm resistors in parallel. The 4//8=8/3 ohms.
i1=24/(8/3+4)=3.6 A
We obtain i(t) from t1, using current division, by writing,
i(t)= 3.6*4/(4+8) = 1.2A, t<0
Since the current through the inductor cannot change instantaneously, i(0)=i(0-)=1.2A
When t=0, the switch is open and the voltage source is disconnected. Now we have a circuit with 4 ohm in series with the 4H inductor and the 8 ohm resistor.
Req=4+8=12 ohms
T(tow)=L/R=4/12=1/2 seconds
io(t)=io(0)e^(-t/tow)
io(t)=1.2e^-3t
The solution manual shows that io(0)=1.4118 A. I am not sure how they obtained it. I will post the solution for reference as well. Can someone tell me where I went wrong?
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