Explain the concept of initial and final conditions in switching for L and C.

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Explain the concept of initial and final conditions in switching for L and C.

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i) Inductor: The current through an inductor cannot change instantly. If the inductor current is zero just before switching, then whatever may be the applied voltage, just after switching the inductor current will remain zero. i.e the inductor must be acting as open-circuit at instant t = 0. If the inductor current is I0 before switching, then just after switching the inductor current will remain same as I0, and having stored energy hence it is represented by a current source of value I0 in parallel with open circuit. As time passes the inductor current slowly rises and finally it becomes constant. Therefore the voltage across the inductor falls to zero [vL=LdiL/dt=0]. The presence of current with zero voltage exhibits short circuit condition. Therefore, under steady-state constant current condition, the inductor is represented by a short circuit. If the initial inductor current is non-zero I0, making it as energy source, then finally inductor is represented by current source I0 in parallel with a short circuit.

ii) Capacitor: The voltage across capacitor cannot change instantly. If the capacitor voltage is zero initially just before switching, then whatever may be the current flowing, just after switching the capacitor voltage will remain zero. i.e the capacitor must be acting as short-circuit at instant t = 0. If capacitor is previously charged to some voltage V0, then also after switching at t = 0, the voltage across capacitor remains same V0. Since the energy is stored in the capacitor, it is represented by a voltage source V0 in series with short-circuit. As time passes the capacitor voltage slowly rises and finally it becomes constant. Therefore the current through the capacitor falls to zero[iC=CdvC/dt=0]. The presence of voltage with zero current exhibits open circuit condition. Therefore, under steady-state constant voltage condition, the capacitor is represented by a open circuit. If the initial capacitor voltage is non-zero V0, making it as energy source, then finally capacitor is represented by voltage source V0 in series with an open-circuit.

The initial and final conditions are summarized in following table: 