welcome to engineering funda family this video is a part of network theory lecture series and in this video i'll be going to explain you what is cut set what is fundamental cut set and what is cut set matrix now my dear students to understand what is cut set matrix you should know what is fundamental cut set and to understand what is fundamental cut set you should have basic idea about what is cut set so let me explain you first what is cut set my dear students whenever any graph is given to you from that graph if you remove some branches then there may be bisection of graph into two parts so cut set is what cut set is removal of some branches from the graph to bisect graph into two parts this two parts may not be equal or identical but here you just need to bisect graph into two parts for that you will have to remove some branches so you see cut set is having removal of some branches so here we remove some branches which may or may not be identical to each other and it bisects graph into two division let me explain that by one example so it will be more clear so you see here we are having one graph in which if you remove some branches then you can bisect graph into two parts so let us say i am removing branch a branch b and branch c then you will be having node one that is a one part of graph which will not be connected with this second part of graph which will be having links e d and f let me show you that so you can observe in one cut set we are removing branch abc so if you remove branch abc you can observe here this part of the graph which is having node 1 which is not connected with this part of the graph right so that is how you can provide cut set there can be many example which is there with this graph let me give you one more example with this same graph if you remove branch a e f in that case this node 3 will not be connected with these branches which are b c and d let me show you graphically first so as if you remove a e and f in that case you can see this node 3 that is a part of graph which is not connected with another part of graph right so here all you do is you remove some branches and you bisect graph into two divisions so that is cut set now let us try to understand what is fundamental cut set so as you know cut set is what in cut set we remove some branches but when we talk about fundamental cut set so in that first of all you will have to see the tree which is given in the graph after that when you provide cut set then that should contain one tweak and the rest link that will be fundamental cut set and based on fundamental cut set we can form cut set matrix so i need to explain you how we can have fundamental cut set by one practical example so for that here i am having one graph in which let us consider one tree so when you have a calculation of tree at a time first of all you should know how many branches are there with given graph with tree so when you want to calculate number of branches in tree then that will be total number of nodes minus one so here total four nodes are there so total number of branches entry will be 3 it will be 4 minus 1 and here given tree should not have any closed loop right so here what i am doing is i will be considering one tree which is b e and d and this b e d tree is not forming any closed loop and it is having three branches let me explain you by that drawing first so you can observe here with this given graph this is one example of tree in which total links are 3 right and whenever you plot tree then other than the branches which are there in tree those are link and the branches which are there with tree those are twigs so here with this tree twigs are b e and d and here you see with this graph a c and f that is not a part of this tree so you can say those are links so my dear students you see i have drawn links with dashed line and those are a c and f now once you have graph with respect to tree we can identify fundamental cut set so you should know that the cut set that contains one tweak and the rest link that will be fundamental cut set so my dear students here you will have to see one twig and rest link so you see with respect to tweak b if you provide cut set over here then you see with this cut set c1 there is one twig and two links right so you can say this is cut set one and this cut set one that is having one tweak that is b and rash link those are a and c so you can say this is twig and a and c those are link now if you observe over here at node 3 we are having one tweak that is e and if you provide cut set over here then there will be one tweak that is e and two links those are a and f so you can observe here with cut set two we are having one tweak that is e and two links those are a and f now if you see with tweak d if you provide cut set over here then with this cut set which is cut set 3 you will be having one tweak over here and two links so tweak is d and links are c and f with this cut set three so here with this cut set three d is one tweak and this c and f those are linked so my dear students when you want to understand what is fundamental cut set so at that time it will be cut set with respect to tree in which it should have one twig and rest link so here i have shown you one practical example now my dear students what i'll do is i'll explain you cut set matrix and i'll be considering same example in which i'll derive cut set matrix so let me explain you first what is cut set matrix so my dear students cut set matrix represents orientation of branches with respect to fundamental cut set so cut set matrix represents orientation of branches and that we the that we represent with respect to fundamental cut set and direction of cut set that will be there in the direction of twig of fundamental cut set this is very essential you should know direction of cut set that is there in the direction of twig of fundamental cut set i'll show you that by practical example so that will be more clear so you see here we are having three cuts at c1 c2 c3 which i have already explained you right in which when you want to show direction of cut set c1 c2 and c3 then it should be there in the direction of twig so see for cut set c1 twig is there in inward direction over here so direction of cut set that should be there in inward direction you see over here i am plotting it if you see this cut set c2 in which we are having twig e which is there in inside direction so cut set 2 that will be there with inside direction as you can see it over here right now when you talk about cut set 3's direction then you see it is having to big d which is there in outward direction so direction of cut set that should be there in outward direction as you see i am showing it over here so that is how we can have direction of cut set as per this basic definition now how to write elements so for that you will have to write plus 1 when direction of branch is there in the direction of cut set and when direction of branch is there in opposite direction to the direction of cut set then you should write minus 1 and you will be writing 0 when branch is not connected with cut set so let us try to understand that with this practical example so here when you want to write cut set matrix then vertically you will have to write cut set here we are having three cut set c1 c2 and c3 and horizontally we will be writing branches so here we are having six branches a b c d e f now when you want to write elements in cut set matrix then you will have to see cut set wise diagram so let us see first c1 so you see in c1 direction of b that is there in the direction of cut set so here i need to write plus one you can observe direction of a that is there in opposite direction to the direction of cut set so i should be writing minus 1 with a then you see this c that is there in opposite direction to the direction of cut set so here i should be writing minus 1. and d e f are not connected with this cut set c 1 so i should be writing 0 over here now let us see what is happening with cut set 2 so with c 2 you see this a which is there in the direction of cut set c2 so i can say a is plus 1 this e that is also there in the direction of cut set c2 so you see e will be also plus 1 and you see f is there in opposite direction to the direction of cut set so i can say here there will be minus 1 and b c d are not connected with cut set so that will be 0. now let us see what is happening with cut set c3 so you see with cut set c3 you can observe c branch is there in opposite direction to the direction of cut set so i can say c is minus 1 you see this d that is there in the direction of cut set so d will be plus 1 and you see this f that is there in opposite direction to the direction of c 3 so f will be minus 1 and a b and e are not connected with cut set c3 so i can say those are zero so that is how we can form cut set matrix so my dear students here these are the basics that you should take care of when you calculate cut set matrix in next video i'll explain you few essential properties of tie set matrix and cut set matrix after that i'll explain you how we can form kvl and kcl equations based on tie set matrix and cut set matrix i hope you have understood this thank you so much for watching this video