Initial Conditions

Initial Conditions

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  Initial Conditions Branch : Div.: Prepared by : - Guided By: Circuit and Network
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  INITIAL CONDITIONSINITIAL CONDITIONS In Initial conditions, we find the change in selected variables in a circuit when one or more switches are moved from open to closed positions or vice versa.  t=0- indicates the time just before changing the position of the switch  t=0 indicates the time when the position of switch is changed  t=0+ indicates the time immediately after changing the position of switch
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  INITIAL CONDITIONS 1.1. RESISTORRESISTOR The voltage current relation of an ideal resistance is V=R*I  From this equation it can be concluded that the instantaneous current flowing through the resistor changes if the instantaneous voltage across it changes & vice versa  The past voltage or current values have no effect on the present or future working of the resistor i.e.. It’s resistance remains the same irrespective of the past conditions
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  INITIAL CONDITIONS 2. INDUCTOR2.INDUCTOR  The expression for current through the inductor is given by
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  Hence if i(0- )=0A, then i(0+ )=0A So we can visualize inductor as a open circuit at t=0+
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   If i(0- )=I0, then i(0+ )=I0 i.e. the inductor can be thought as a current source of I0 as shown
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  INITIAL CONDITIONS
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  • If V(0- )=0V, then V(0+ )=0V indicating the capacitor as a short circuit • If V(0- )= V volts, then the capacitor can be visualized as a voltage source of V volts
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  EXAMPLE-1 :EXAMPLE-1 :In the network shown in the figure the switch is closed at t=0. Determine i, (di/dt) and (d2 i/dt2 ) at t=0+ . At t=0- , the switch is Closed. Due to which il(0- )=0A Vc(0- )=0V
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  At t=0+ the circuitis From the circuit il(0+ )=0A Vc(0+ )=0V
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   Writing KVLclockwise for the circuit Putting t=0+ in equation (2)
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   Differentiating equation(1) with respect to time