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Initial Conditions for the 2nd Order Circuits

Initial Conditions for the 2nd Order Circuits - v t or i t...

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Q: Determine the Initial Conditions for the 2 nd Order Circuits. v 0   i 0   d v 0   dt or d i 0   dt Step 1 First thing you need to determine is the Capacitor Voltage and the Inductor Current at time t=0- (Before the switch is closed/opened), namely v C 0 −  and i L 0 −  . Then by Continuity, v C 0   = v C 0 −  and i L 0   = i L 0 −  . If the initial conditions v C 0   and i L 0   are given, then SKIP this step. Step 2 To Find v 0   or i 0   , you need to come up with an equation that relates v 0   or i 0   with one of the two above initial conditions. Chances are, to find v 0   , you will need to equate v 0   to i L 0   and to find i 0   , you will need to equate i 0   to v C 0   . Step 3 To Determine d v 0   dt or d i 0   dt , you most likely need to write the FIRST equation that you will need for determining the Differential Equation for the response
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Unformatted text preview: v t or i t , which is either a KVL equation or a KCL equation. Step 4 Now you will need to inspect the KVL or KCL equation and see what variables are known at time t=0+. At this point, the known variables are usually v t and v C t , or i t and i L t . For the unknown variable(s), you will need to use these analysis tools to find an equation consists of the unknown variable and the Desired Initial Conditions: Ohm's Law, Device Laws, KVL, or KCL. Solve the Desired Initial Conditions, d v dt or d i dt . Note: You might need to Differentiate to get the Desired Initial Conditions, d v dt or d i dt DONE!!!...
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