Initial Conditions_Circuit and Networks

1. Initial Conditions
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Circuit and Network

2. 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

3. 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

4. INITIAL CONDITIONS
2. INDUCTOR2. INDUCTOR
 The expression for current through the inductor is
given by

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

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

8. INITIAL CONDITIONS

9. • 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

11. 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

12. At t=0+
the circuit is
From the circuit
il(0+
)=0A
Vc(0+
)=0V

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

14.  Differentiating equation (1) with
respect to time