we have completed KVL and KCl and now we are going to understand what is mesh analysis and how to perform the mesh analysis and the first question is why we use mesh analysis what is the use of mesh analysis and to get the answer of this question we need to understand the very basic requirement to analyze any electrical network when we analyze any electrical network our main aim is to obtain the power delivered or the power absorbed by different electrical elements and to have the power delivered or the power absorbed we need the voltage and we need the current and using the mesh analysis we can have the unknown currents in the electrical Network so to obtain the values of unknown currents in the electrical Network we perform the mesh analysis so let's begin our discussion and first we will understand what is mesh and then I will give you all these steps required to perform the mesh analysis mesh is a loop mesh is a loop and this loop is not a normal loop this loop does not contain any inner loop so whenever you have a loop having no loops inside then you will call the loop a mesh and we know what is a loop loop is a part having the first node and the last node same and I hope from this definition you now know what is a mesh and you can identify mesh in a given network now we will move on to the steps required to perform the mesh analysis step number one is to identify the total number of meshes you will be given in network and in that network you need to identify total number of Masha's we know what is a mesh it is a loop having no loops inside so you simply need to identify the total number of such loops in the given network and once we are done with identifying the total number of meshes in step number two we assigned the mesh currents mesh current is the current that flows only around the perimeter of a mesh so all the meshes which we have identified will have their individual mesh currents so this is all four first step and the second step let's move on to the third step in the third step we are required to develop the KVL equation for each mesh and in the fourth step we need to solve the KVL equation which we have developed to find the mesh currents which we assigned in step number two so these are the four steps involved in performing the mesh analysis and once we have the mesh currents we can perform the required calculations according to the given question now before solving one example and before implementing all these steps there are few important points which you need to know the first point is mesh analysis is only applicable for planar networks now what is a planar network for example here we have a network and in this network you can see that this particular branch is crossing this branch so this network is non planar why because we don't have the whole network placed on a plane why because this branch is crossing this branch so no branch should cross another branch and when this happens we will call the network cleaner network this network and this network is same instead of having this particular branch crossing this branch we have drawn it like this and therefore we have a planar Network and in this network we cannot obtain different currents by using the mesh analysis mesh analysis is not applicable in this network but mesh analysis is applicable in this network so this is what do we mean by mesh analysis is only applicable for planar networks this is all for the first point according to the second point the direction of the mesh current can be clockwise or it can be anti clock wise it is up to you which direction you want to choose but I will select the clock wise direction I will not select the anti-clockwise direction I will prefer clockwise direction there are two reasons the first reason is it is psychological having a clock wise direction is more convenient to look at and to handle as compared to a current which is anti-clockwise and the second important reason is generally in the network for example in this network the source is located on the left hand side and therefore current will have this direction and when you choose the clockwise direction this direction is same as this direction therefore you will get the positive value of the current and if you choose the anti-clockwise direction the current obtained will be negative therefore we assign the clockwise direction to different mesh currents let's move on to the third point according to the third point the number of equations required to solve an electrical Network using the mesh analysis is equal to the number of meshes and the number of meshes is equal to the branch - number of nodes minus one so remember this formula is the number of equations M is the number of meshes B is the number of branches we are having in the network n is the number of nodes and when you perform B minus n minus 1 you will have the number of meshes and it is same as the number of equations required to solve an electrical network using mesh analysis so I hope the Third Point is also clear to you now it is time to solve one example problem using the mesh analysis and we know in step number one we identify the total number of meshes so let's quickly identify the total number of meshes in this circuit we have 1 & 2 meshes you cannot consider the outer loop as a mesh because it is having 2 different loops inside it so according to step number one we have total 2 meshes and if you look at step number 2 you will find we now need to assign the mesh currents and we know the direction of the mesh current is clockwise we will take the direction has clockwise let's say in the first mesh current i1 is flowing and the direction of current i1 is clockwise and in the second mesh current i2 is flowing and the direction of current I 2 is also clockwise so we are done with the second step also and in the third step we are required to develop the KVL equation for each mesh and in the fourth step we are required to solve the KVL equations to find the mesh currents so let's develop the KVL equations for the two meshes and we will start with the first mesh from this point moving in the direction of the mesh current i1 when we move in this direction we will have +10 volts plus 10 volts then we have current i1 flowing through resistance having the value 5 ohms therefore we will have minus i1 multiplied to 5 or we can write 5 times i1 and the polarity will be plus minus now we will move further and this time current i1 is flowing through 5 ohm resistor but I 2 is also flowing through this resistor I 1 is flowing in this direction from top to bottom and high 2 is flowing in this direction from bottom to top now what will be the net current i1 minus i2 or I 2 minus i1 this is the most important point in this lecture we are developing the KVL equation for the first mesh and the first mesh is having its mesh current as i1 therefore while writing down the KVL equation for the first mesh we will give the priority to the mesh current of the first mesh that is I 1 therefore we will consider the net current to be i1 minus i2 i1 is greater than I two therefore we have minus five times i1 minus i2 now moving forward we will reach to the same point therefore we will equate this sum with zero now when you simplify this you will have two times i1 minus i2 equal to two let's call this equation number one now let's develop the KVL equation for the second mesh and we will start from this point and you can see that when moving in the same direction of i2 again we have the same condition whether to choose I 1 minus I 2 or I 2 minus I 1 as the net current through five ohm resistor and like I said earlier we give priority to the mesh current whose KVL equation we are writing down and this time we are writing the KVL equation for the second mesh and therefore we will give the priority to current i2 and not to current i1 we will assume current I 2 is greater than current i1 therefore we will select this to be net current and hence we have minus 5 i2 minus i1 in the first case and this was the polarity of the voltage drop across this resistor and in the second case this is the polarity of the voltage drop across this resistor and therefore we have minus v i2 minus i1 after this we have minus 10 multiplied to i2 minus 10 multiplied to i2 and this sum will be equal to 0 now when you simplify this you will have I 1 minus 3 times i2 equal to 0 let's call this equation number 2 and this is time to solve the KVL equations we have obtained in step number 3 so in step number 4 we will perform the operation equation 1 two times equation two and this will give us current i2 equal to two over five amperes and now we have the current flowing through ten ohm resistor and we are required to calculate the power loss in the 10 ohm resistor so there is no need to calculate current i1 however you can easily calculate current i1 and just put the value of current I 2 in equation number two or in equation number one but we will directly calculate the power loss or the power dissipated it is equal to the square of the current that is I 2 square multiplied to the resistance corresponding to which we are calculating the power loss or power dissipated so we have 2 over v square multiplied to 10 watts when you solve it you will get 1.6 watts so this is the answer and we have obtained it using the mesh analysis so I hope mesh analysis is clear to you the very important thing is this particular point you have to remember that while drawing the KVL equation for a particular mesh you have to consider the mesh current to be the largest these points will become more clear when we will solve more questions in the coming lectures [Applause] [Music]