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

INITIAL CONDITIONS INITIAL 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.

• 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.

• Initial condition focuses 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.

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

2. . INDUCTORINDUCTOR The expression for current through the

inductor is given by

Hence if i(0-)=0A , then i(0+)=0ASo we can visualize inductor as a open circuit at t=0+

• If i(0-)=I0 , then i(0+)=I0 i.e. the inductor can be thought as a current source of I0 as shown

FINAL CONDITIONS :FINAL CONDITIONS : 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

3. CAPACITORCAPACITOR The expression for voltage across the

capacitor is given by

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

• Final ConditionsFinal Conditions 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.

EXAMPLE-1 : In the network shown in the figure the switch is closed at t=0. Determine i, (di/dt) and (d2i/dt2) at t=0+ .

At t=0- , the switch isClosed. Due to whichil(0-)=0A

Vc(0-)=0V

At t=0+ the circuit is

From the circuit il(0+)=0A

Vc(0+)=0V

• Writing KVL clockwise for the circuit

Putting t=0+ in equation (2)

• Differentiating equation (1) with respect to time

THANK YOU

Thermocouples 18