Question
Asked Apr 1, 2019
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In the following circuit, use either differential equation approach or the shortcut method to find
io(t) fort 0. State which method you are using.
62"
kV
12
o (t)
t 0
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In the following circuit, use either differential equation approach or the shortcut method to find io(t) fort 0. State which method you are using. 62" kV 12 o (t) t 0

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Expert Answer

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Step 1

STEP BY STEP METHOD:

From the circuit, write the expression for io(t) as follows:

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Step 2

Here,

io(∞) is the current through the required branch (6 kilo ohms branch) at final state,

io(0+) is current through the required branch for t =0+, and

τ is the time constant for t >0.

From the given circuit, the switch opens at t =0. That is, switch is in closed condition before t =0. The inductor gets short circuited as the switch was closed for a long time. Therefore, redraw the circuit for t =0- as shown in Figure 1 and find the value of current through the inductor for t =0-.

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Step 3

From Figure, it is clear that, the current in the circuit flows only through the short circuit path of ind...

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