Initial Conditions

Initial Conditions

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  Name :- Suraj.B.Rawat-Suraj.B.Rawat -140410109085140410109085 Smit Shah -Smit Shah -140410109096140410109096 S.Y electrical 2S.Y electrical 2 Sem 3Sem 3 Subject:-Circuits and NetworksCircuits and Networks Topic :-Initial ConditionsInitial Conditions
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  INITIAL CONDITIONSINITIAL CONDITIONS:: ImportanceImportance • Differential Equations written for a network may contain arbitrary constants equal to the order of the differential equations. • The reason for studying initial conditions is to find the value of arbitrary constants that appear in the general solution of differential equations written for a given network.
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  • In Initialconditions, 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 conditionfocuses solely on the current and voltages of energy storing elements (inductor and capacitor) as they will determine the circuit behavior at t>0. • PAST HISTORY OF THE CIRCUIT WILL SHOW UP THE CAPACITOR VOLTAGES AND INDUCTOR CURRENTS.
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  1.1. RESISTORRESISTOR  Thevoltage 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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  2.. INDUCTORINDUCTOR  Theexpression 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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  FINAL CONDITIONS :FINALCONDITIONS :  From the basic relationship V= L*(di/dt) We can state that V=0 in steady state conditions at t= as (di/dt)=0 due to constant current
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  3. CAPACITORCAPACITOR  Theexpression for voltage across the capacitor is given by
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  If V(0- )=0V ,then V(0+ )=0V indicating the capacitor as a short circuit
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  If V(0- )= Vvolts, then the capacitor can be visualized as a voltage source of V volts
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  • Final ConditionsFinalConditions The current across the capacitor is given by the equation i=C*(dv/dt) which indicates that i=0A in steady state at t= due to capacitor being fully charged.
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  EXAMPLE-1 : Inthe 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
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  THANK YOU Thermocouples 18