Hey friends, welcome to the YouTube Channel 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=Ldi/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= Ldi/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= CdV/dt Provided that this capacitance is not changing with time. So, we can say that the current i is nothing but i=CdV/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= Cdv/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= Ldi/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.