in this presentation we are going to discuss our next network theorem which is tavin ins theorem and as the name is suggesting this theorem was given by Lyon choice Thevenin who was a French engineer and in 1883 he developed the tenon equivalent circuit and before we move on to the equivalent circuit and the statement of the tavern Sturm we will first understand why Evan ins theorem is needed it often happens that a particular element in a circuit is variable while the other elements are fixed each time the variable element is changed the entire circuit has to be analyzed again to avoid this problem Thevenin theorem provides a technique by which the fixed part of the circuit is replaced by an equivalent circuit so it is very easy to understand that in a large complex network there is one element which is variable while the other elements are fixed and when this variable element is changed the analysis has to be done again now to avoid this problem we replace the fixed part of the circuit by the equivalent circuit known as the Thevenin equivalent circuit and this equivalent circuit is very simple and therefore when the variable part is changing we do not have to perform the tedious calculations again all these points will become crystal clear by the end of this lecture now we will move on to this statement of Thevenin theorem according to the statement a linear bi-directional to terminal Network can be replaced by an equivalent network consisting of a voltage source V th connected in series with a resistor R th so as I said earlier Thurman's theorem provides a technique by which we can replace the fixed part of the circuit by the equivalent circuit and the equivalent circuit or network will have V th connected in series with rth so you can think about the simplicity this theorem as providing what is Vth and what is hard eh Vth which is known as the Thevenin Sportage is open circuit voltage at the terminals we will understand how we can calculate V th in the network and the rth which is known as the Thevenin resistance is the input or equivalent resistance at the terminals when the independent sources are turned off and we will understand how to calculate Vth and rth by taking one example to summarize our discussion till this point I have taken this particular arrangement in which we have linear and bi-directional network which is having fixed elements and from this network we are getting two terminals across which one load is connected and this load is a variable load and therefore for the simplicity it is good to have the Thevenin equivalent circuit in place of this network and we know what is seven ins equivalent circuit it is v th connected in series with rth so here we have replaced this particular network by v th connected in series with rth you now the only problem is we don't know how to find out Vth and how to find out heart eh for this I have taken one example in which we are required to find out the current flowing through this load resistor which is variable in nature when it is equal to 6 ohms and it is equal to 16 ohms I want you to analyze the given circuit for some time and then we will move on to the solution I hope you are done now we will move on to the calculation of current flowing through RL when it is equal to 6 ohms and it is equal to 16 ohms and to find out the current we will first find out the Thevenin equivalent circuit and we know to find out havin an equivalent circuit we need V th and we need R th so first we will find out seven ins voltage v th and for this purpose we will make one modification in our network and the modification is we will remove the load resistance and we will open circuit the branch like this and we are doing this because we th is the open circuit voltage between these two terminals and to remember one thing always take the polarity like this and keep the polarity like this in the equivalent circuit as well do not reverse the polarity in the equivalent circuit keep it like this now we will find out V th in this modified Network if we talk about the current flowing in this branch then it will be 0 why because this branch is open circuited and if I assume the potential at this node equal to 0 then potential here will be V th no drop will be there across this resistor because current is zero and in this there are no resistors therefore no voltage drop will be there in this wire and potential at this node will be equal to V th and therefore if we can find out the potential at this node we can have V th and to find out potential at this node we will use nodal analysis this is our reference node and this is our principal node and let's say the potential at principal node is equal to V sub X and we know we assume the potential at principal node to be the largest potential in the network therefore all the currents in the branches connected to this node will leave this node let's say this is our current i1 this is current i2 and this one here his current i3 now from KCl we will have i1 plus i2 plus i3 equal to zero to find out ivan we need the potential at this node which will be 32 volts and I 1 it will be equal to VX minus 32 divided by 4 then we have plus i2 i2 it will be equal to VX minus 0 divided by 12 so we have VX divided by 12 then we have plus i3 i3 will flow like this this means i3 is the current moving in this direction in this branch and it is opposite to the direction of 2 amperes current flow therefore we will have i3 equal to minus 2 now doing some rearrangements here we will have 3 times VX minus 96 plus VX equal to 24 in the next step we will simplify this further we will have 4 VX equal to 120 therefore VX is equal to 120 divided by 4 which is 30 folds and in this way we have obtained the Thevenin sportage Vth is equal to VX and therefore Thevenin z-- voltage VT H is equal to 30 volts now we will move on to the calculation of Thevenin equivalent resistance and to calculate rth we will do some modifications in our network and the modification number one is same modification we did case of calculating Vth with a open circuit the load resistance and the modification number two is turning off all the independent sources this is our first independent source we will turn it off by replacing it with a short circuit like this and this is our second independent source and we will turn it off by replacing it with an open circuit and then we will calculate the equivalent resistance between the two terminals when looked from the side and this equivalent resistance is known as rth the Thevenin equivalent resistance and when you observe the modified network you will find four ohms resistor and 12 ohms resistor they are in parallel so R th it will be equal to four parallel with twelve and their equivalent their equivalent is ten in series with one ohm resistor so we will have plus one from here we will have R th equal to four multiplied to 12 divided by 4 plus 12 plus one when you solve it he will have rth equal to four ohms so in this way we have calculated the Thevenin equivalent resistance and we already calculated the Thevenin voltage and therefore now we can have the Thevenin equivalent circuit this circuit will have the Thevenin voltage which is equal to 30 volts which is connected in series with the Thevenin resistance which is 4 ohms and we will have them connected to our would resistance so this circuit is our Thevenin equivalent circuit and with the help of this equivalent circuit we are required to find current flowing to RL when it is six homes and 16 ohms so first we will assume the current flowing through RL to be I sub L and in case number one when RL is equal to 6 ohms we will have Eyal equal to 30 volts divided by 4 plus RL which is 6 so I L is equal to 30 divided by 4 plus 6 so we have 3 amperes in case number two when RL is equal to 16 ohms hi L will be equal to 30 divided by 4 plus 16 30 divided by 4 plus 16 this will give us 1 point 5 amperes so you can notice that even after changing the value of one element the calculations are pretty simple to do and this is because we have Thevenin equivalent circuit so I hope you know understand what is the valence theorem and in the coming lectures we are going to solve more questions on 7 ins theorem so this is all for this lecture see you in the next one