Solve Confusing Inductor Question: Finding Parts b,c,d - Help Needed

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tesla58
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Summary: Confusing Inductor question

Circuit diagram of three inductors, 1 H, 4 H and 3.2 H, with black box output voltage v0 and switch at t = 0, with current labels i1, i2 and i0 shown.
I've been in trouble with a question for whole days , trouble is finding parts b,c and d.
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Worked solution showing i0(0) = -(i1(0) + i2(0)) = -(-6 + 1) = 5 A, boxed; Leq = 1||4 = 0.8 H; Leq + 3.2 = 4 H; and i0(t) = -(1/4) integral of 2000e^(-100 tau) plus 5, evaluated to 5e^(-100t) A, boxed.
in the solving of part b WHEN we find i0(t) ,why minus is in front of integral(-1/4 coefficient one) and why +5 why not -5 ? I think it relates passive sign convention but i do not know how to determine it.

Handwritten-style derivation of inductor voltage and current in parts c and d: v3.2 = 3.2(-100(5)e^(-100t)) = -1600e^(-100t) V, vLeq = v3.2 + v0 = 400e^(-100t) V, i1(t) = -4e^(-100t) - 2 A, i2(t) = -e^(-100t) + 2 A.
and also part c VLeq = V3.2 + V0 where does this equation come from ? Please some help and sorry for the bad english and if i open the thread to wrong place.
 

Discussion

Hi.
tesla58 said:
in the solving of part b WHEN we find i0(t) ,why minus is in front of integral(-1/4 coefficient one) and why +5 why not -5 ? I think it relates passive sign convention but i do not know how to determine it.
Voltage and current here do not seem to follow usual sign convention, "current flows from voltage + to voltage -". I think it is the reason why.

tesla58 said:
where does this equation come from ?
It also comes from sign convention of currents. Oposite direction of ##v_{3.2}## and ##v_0## comes from opposite direction definition between current ##i_0## and currents ##i_1## and ##i_2## .
 
Hint: Determine what element is in black box, and find its value, setting t=0 in the equation v(t)=2000*e^-100t
 
In my opinion the KVL circulation it has to be:
-3.2*dio/dt+vo+1*di1/dt=0 and if
di1/dt+di2/dt=-dio/dt and 1*di1/dt=4*di2/dt then
dio/dt*(3.2+0.8)=-Vo
At t=0- Vo=0 [the switch is still close].
io[0-]=5
Circuit schematic with two inductors, 1 H and 4 H, in parallel with currents i1 and i2, in series with a 3.2 H inductor carrying current io, and a switch at t = 0 feeding a black box with voltage vo.

io=-1/4∫vo|t=0+ to t=t| +5[io t=0-]
 
I think I found a way. İt is about which one supply power to the circuit and which one receive. So here i1(0)=-6
in the beginning the most big current 6 amp it means that it supply power to the circuit ,according to sign convention current must be the direction of voltage increase and we also should consider that i1 acctually downward.And i0 must receive power so its current direction is direction of voltage drop.Finally we implement KVL
analysis.
Circuit schematic labeled Figure P6.25 showing two parallel inductors of 1 H and 4 H with currents i1 and i2, a switch closed at t = 0, a 3.2 H inductor carrying current io, and a black box with terminal voltage vo.
 
1. guess a really simple component for the black box
2 .then the given v(t) is a big hint once you've found i(0)
3. Verify that your guess is correct by computing a time constant involving the inductors and the black box.

The rest is straight-forward.