Explain the concept of initial and final conditions in switching circuits for elements R and L.

Explain the concept of initial and final conditions in switching circuits for elements R and L. 
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1 Answer

Answer :

Concept of Initial and final condition in switching circuits for R: 

Consider a resistor is connected to a voltage source, using a switch as shown in fig below

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The switch is closed at time t = 0, so we get V= iR which is time independent equation. Here current changes as per voltage without any time delay. There is no change in the value of resistor R, it remains same for initial condition and final condition.

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Concept of Initial and final condition in switching circuits for L:

Consider a inductor is connected to voltage source as shown in fig below:

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The property of inductor is to oppose any change in current. So the current through an inductor cannot change instantaneously. There are 2 cases.

i) If no initial current is passing through inductor, then at t= 0+, it acts as open circuit. The final condition is given by the equation vL =L di/dt. At t=∞, it acts as short circuit.

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ii) If initial current is passing through inductor, then at t= 0+, it acts as constant current source of value I0

At t=∞,( final condition),the inductor acts as current source of value Io in parallel with short circuit.(I0 is the current in inductor just before switching)

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