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ALL ABOUT ELECTRONICS. So, today we are going to start a new topic,
that is transient analysis in the circuit, which will be covered in 3-4 videos. So, in this video, we will understand what
do we mean by this transient analysis, what is the importance of this transient analysis,
and we will see the behaviour of the basic circuit components during this transient. So, first of all, let's understand what do
we mean by this transient. So far, in the circuit analysis, we had assumed
that the voltage source is connected since a long time in the circuit. That means the circuit has attained the steady
state condition. That means voltage and current in the circuit
have attained the steady state condition. But for the first time when we are connecting
this voltage source to the circuit, then circuit takes a time to reach its steady state value
for this voltage and current. Similarly, let's say the voltage source is
connected to the circuit since a long time and circuit has attained the steady state
condition. And the voltage and current in the circuits
are let's say V1 and I1. Now, if you suddenly removes this voltage
source from the circuit, then the circuit will attain new values of this voltage and
current. Thar is V2 and I2. But to reach this new values of this V2 and
I2, the circuit will take some time. So, this time or this transition time is known
as transient. So, this transition period or transient time
is a very short amount of time, which is in the range of microseconds up to the few milliseconds. So, as we know what do we mean by this transient
time or transient, let's understand what is the importance of this transient. And why do we study this transient analysis
in the circuit? So, let's say you have one circuit and in
this circuit, let's say suddenly some spike or surge comes into the circuit. Now, because of this surge, it might happen
that some components in the circuit might get failed. So, it is necessary to see the behaviour of
the circuit when something abruptly changes in the circuit. And how the circuit behaves to this abrupt
changes. And to see the behaviour of the circuit to
this abrupt changes, it is necessary to see the voltage and current during this abrupt
changes, or during this transients. So, if we analyse the voltage and current
during this transient, then we can know how the circuit behaves to this abrupt changes. And whether our circuit will able to sustain
such transients. So, apart from that, design point of view
also, this transient analysis is quite important. And particularly in the switching applications. So, let's say you are using a transistor as
a switch. So, it is important to understand the behaviour
of the transistor, how fast it goes from on to the off state. So, in design point of view also, this transient
analysis is quite important. Alright, so now let's see the behaviour of
the basic components like resistor, capacitor and inductor for this transient conditions. So, we will see, how these basic components
behave during this transients. So, let's say we have one resistor R.
And at time t=0, this resistor R is connected to some voltage source V. So, before this time t=0, let's say time t=0-,
which is the time just before the switch has been closed. So, at this time, the current through this
resistor R is 0. Now as soon as we close this switch at time
t=0, the current I will start flowing through this circuit. And this current I can be given as, V/R.
So, as soon as we close this switch at time t=0, suddenly the current will start flowing
through this circuit. So, at time t=0+, which is the just after
the switch has been closed, the current through this resistor R can be given as, V/R.
So, we can say that this resistor reacts instantaneously to this rate of change of current or rate
of change of voltage. Similarly, let's see the behaviour of the
inductor during this transient. So, before this time t=0, no current is flowing
through this circuit, as there is no voltage source connected to this circuit. At time t= 0, the switch has been closed. Now, we know that the voltage across the inductor
can be given as, VL= L*(di/dt)
So, the voltage across the inductor is proportional to the rate of change of current. So, as soon as we close the switch at t=0,
suddenly the current will start flowing through this inductor. Or we can say that in no time the current
will start flowing through this inductor. And this time dt tends to zero, this di/dt
tends to infinity. Which corresponds to the voltage across the
inductor tends to infinity. So, practically, which is not possible. So, we can say that this inductor opposes
the instantaneous change of current. So, whatever current that is flowing through
this inductor at t=0-, the same current will flow through the inductor at t=0+. That means, just after you have closed the
switch. So, at t=0-, if the current that is flowing
through this inductor iL is zero, then the same current will flow through the inductor
at time t=0+. So, we can say that at time t=0+ this inductor
will act as an open circuit. Similarly, let's say voltage V is applied
across this inductor continuously, since a long time. And let's say the current I0 is flowing through
this inductor. Now, at time t=0, this voltage source has
been removed from this circuit. So, as we have already seen earlier, this
inductor opposes the instantaneous change of current. So, at time t=0-, current that is flowing
through this inductor is I0. So, as the inductor opposes the instantaneous
change of current, so at t=0+ time also, current that is flowing through this inductor will
be I0. So, during this transition period, this inductor
will act as a current source with a value of I0. So, we can say that IL(0+)=IL(0-)=I0
Now, we know that the voltage across this inductor can be given as, VL=L*di/dt. So, once this transition period gets over,
there will not be any change in current. So, at t is equal to infinity, or after very
long time, there will not be any change in the current. So, the voltage across this inductor will
be zero. Or we can say that t is equal to infinity,
this inductor will act as a short circuit. Similarly, in this case also, once the switch
has been closed at t=0, then after sufficient time, let's say t is equal to infinity theoretically,
there will not be any change in the current. So, this voltage VL that is
VL= L*di/dt will be zero. As this term, di/dt will get zero. So, we can say that at t is equal to infinity,
this inductor will act as short-circuit. So, in summary, we can say that inductor opposes
the instantaneous change of current. So, at t=0, if no current is flowing through
this inductor, then at t=0+, this inductor will act as an open circuit. And at steady state, or theoretically at t
is equal to infinite, this inductor will act as a short circuit. Similarly, if current i0 is flowing continuously
at time t=0, then at t=0+, this inductor will act as a current source with the value of
I0. While at t is equal to infinity, this inductor
will act as a short circuit. So, now let's see the behaviour of the capacitor
during this transient. So, before this time t=0, there will not be
any voltage across this capacitor. And at t=0, once the switch has been closed,
this voltage V will appear across this capacitor. Let's say the voltage that is appearing across
this capacitor is V0. That is V0= V. Now, we know that the charge across the capacitor
can be given as q=CV So, the rate of change of charge, that is
dq/dt= C*dV/dt Provided that this capacitance is not changing
with time. So, we can say that the current i is nothing
but i=C*dV/dt
Now, here, as you can see, the current that is flowing through the capacitor is proportional
to the rate of change of voltage. So, as soon as we close the switch, at time
t=0, suddenly this voltage V will appear across this capacitor. And this time dt tends to zero, this term
dv/dt tends to infinity. Which corresponds that this current ic which
is flowing through the capacitor will tend to infinity. So, practically that is not possible. So, we can say that this capacitor opposes
the instantaneous change of voltage. So, whatever voltage that is appearing across
this capacitor at time t=0-, the same voltage will appear across this capacitor at time
t=0+. So, at time t=0-, the voltage across the capacitor
is zero. So, at time t=0+ also, the voltage across
the capacitor will be zero. Similarly, let's say the other case, in which
the voltage V appears across this capacitor continuously. Now, at time t=0, the switch has been moved
from this position 1 to 2. So, as we know that the capacitor opposes
the instantaneous change of voltage, so the same voltage V will appear across this capacitor
at time t=0+ as well. So, at time t=0-, let's say the voltage across
this capacitor is V0. Then at time t=0+ also, the voltage across
this capacitor will remain V0. So, we can say that this capacitor will act
as voltage source during this transient. And once this transient period is over, there
will not be any change in voltage. That means this dv/dt term will be zero. And hence the current Ic will be zero. So, we can say that at time t is equal to
infinity, or practically after a very long time, there will not be any change in voltage. So, the current through this capacitor will
be zero. Or in another term, we can say that this capacitor
will act as an open circuit. Likewise in the first case also, once the
switch is closed, then after sufficient time or theoretically at time t is equal to infinity,
there will not be any change in voltage across this capacitor. That means, in this equation i= C*dv/dt, this
dv/dt term will be zero. And hence, the current through the capacitor
will be zero. So, after sufficient time, or at time t is
equal to infinity, or in steady state condition, this capacitor will act as an open circuit. So, in summary, we can say that te capacitor
opposes the instantaneous change voltage. So, at time t=0, if there is no voltage across
this capacitor, then at time t= 0+ this capacitor will act as a short circuit. While at time t is equal to infinity or in
steady state condition, this capacitor will act as an open circuit. Similarly, let's say if voltage V0 is appearing
across this capacitor in steady state condition, and suddenly if you remove this voltage source
then the capacitor will act as a voltage source of V0 at time t=0+. But in steady state condition once again it
will act as an open circuit. So, the condition of the components at time
t= 0+ is known as the initial condition. And the condition at a time is equal to infinity
is known as the final condition. So, so far we have we have seen the transient
analysis for the basic components which are connected separately. But in the practical circuit, this component
are connected in either series or in parallel in the circuit. So, whenever circuit contains either inductor
or capacitor, and if you write KVL or KCL equation for such circuits, then it will contain the
derivative term. Let's say in this circuit if you write KVL
equation during the transient, then the voltage across this inductor can be given as VL= L*di/dt
So, this derivative term will come into the picture. And if you see the KVL equation for such circuits,
in the form of linear differential equation, which can be given as
di/dt+P*i=Q Where P is nothing but constant and Q represents
the forced excitation in the circuit. So, this forced excitation could be either
AC soure, DC Source or any other kind of excitation to the circuit. So, now if you see the solution of the differential
equation, it contains the two-term one is the particular integral and second
is the complementary function. So, this complementary function represents
the response of the system when there is no source connected in the circuit. Or we can say that it is the source free response
of the circuit. While this particular integral is the response
of the circuit when there is forced excitation in the circuit. Apart fro that this complementary function
represents the transient response of the circuit. Similarly, this particular integral represents
the steady state response of the circuit. So, in the next video we will see, what is
the response of the R-L and R-C circuits for this transient. So, in the next video, we will see the transient
response for this R-Land R-C Circuits, when there is no source connected in the circuit,
that means the source free behaviour as well as with DC excitation. So, we will see the transient behaviour of
these both circuits graphically as well as mathematically. And we will solve some problems based on this
transient analysis.