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modulation
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Homework Statement
Ok, so this isn't a question of how to solve, but rather why the solution works.
Say you have a circuit with 2 inductors in parallel, a 5H and a 20H, in parallel to the inductors is a resistive network with a resistance of 8Ω, and a switch, which has been closed long enough for the inductors to reach DC steady state. The power source is not shown, but initially there is a current through each inductor, 8A through the 5H, and 4A through the 20H. When the switch is opened, the problem asks to find the voltage and current for the inductors, as well as the current through each individual inductor.
Homework Equations
So the solution for the voltage is [tex]v(t)=96(e)^{-2t}[/tex]
, and current for both inductors is [tex]i(t)=12(e)^{-2t}[/tex]
The solution to the current through the individual 5H inductor is
[tex]i_1(t)= \frac{1}{5} \int_{0}^{t} 96(e)^{-2x}dx -8[/tex]
and for the 20H inductor is
[tex]i_2(t)= \frac{1}{20} \int_{0}^{t} 96(e)^{-2x}dx -4[/tex]
The Attempt at a Solution
So what I do not understand is, how does the integral of the voltage, divided by the inductance, subtract the initial current, give the current through an individual inductor over time??
Really curious as to how this is possible mathematically and why??
Am I missing something?
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