Initial Conditions

In this slide describe about Initial condition of electrical circuit , examples , theory fundamentals & more..

1. 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

2. 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.

3. •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.

4. •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.

5. 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

6. 2. . INDUCTORINDUCTOR
The expression for current through the
inductor is given by

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

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

9. 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

10. 3. CAPACITORCAPACITOR
The expression for voltage across the
capacitor is given by

11. If V(0
-
)=0V , then V(0
+
)=0V indicating the
capacitor as a short circuit

12. If V(0
-
)= V volts, then the capacitor can be
visualized as a voltage source of V volts

13. •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.

14. EXAMPLE-1 : In the network shown in the
figure the switch is closed at t=0. Determine i,
(di/dt) and (d
2
i/dt
2
) at t=0
+
.
At t=0
-
, the switch is
Closed. Due to which
i
l
(0
-
)=0A
V
c
(0
-
)=0V

15. At t=0
+
the circuit is
From the circuit
i
l
(0
+
)=0A
V
c
(0
+
)=0V

16. •Writing KVL clockwise for the circuit
Putting t=0
+
in equation (2)

17. •Differentiating equation (1) with respect to
time

18. THANK YOU
Thermocouples 18