Mesh Analysis
Summary
TLDRThis educational video script introduces mesh analysis, a method for analyzing electrical networks to determine unknown currents. It explains the concept of a mesh as a loop without any inner loops and outlines the four steps for performing mesh analysis: identifying meshes, assigning mesh currents, developing KVL equations for each mesh, and solving these equations. The script also highlights that mesh analysis is applicable only to planar networks and emphasizes the importance of choosing the direction of mesh currents. It concludes with an example demonstrating how to apply these steps to calculate power loss in a resistor.
Takeaways
- 🔍 Mesh analysis is a method used to analyze electrical networks by determining the unknown currents flowing through various elements.
- 🎯 The primary purpose of mesh analysis is to calculate the power delivered or absorbed by different components within an electrical network.
- 🔌 A mesh is defined as a loop in a circuit that does not contain any other loops within it, and it is a fundamental concept in mesh analysis.
- 📚 Mesh analysis is applicable only to planar networks, where no branch crosses over another, ensuring the network can be drawn on a single plane without any intersections.
- ✏️ The process of mesh analysis involves four main steps: identifying meshes, assigning mesh currents, developing KVL equations for each mesh, and solving those equations.
- 🔄 The direction of mesh current can be chosen as clockwise or counterclockwise, but a clockwise direction is often preferred for convenience and consistency with typical current flow from sources.
- 📉 The number of equations needed for mesh analysis is equal to the number of meshes, which can be calculated using the formula: number of meshes = (number of branches - number of nodes + 1).
- 🧮 Once the mesh currents are determined, further calculations such as power loss in resistors can be performed using the values obtained from the mesh analysis.
- 📝 When developing KVL equations, the mesh current of the particular mesh being considered is given priority in the calculation of net currents through shared resistors.
- 🔑 A key takeaway is the importance of considering the mesh current as the dominant current when formulating KVL equations for a specific mesh, which affects the calculation of voltage drops across resistors.
Q & A
What is the primary purpose of mesh analysis in electrical networks?
-The primary purpose of mesh analysis is to determine the unknown currents in an electrical network, which is essential for calculating the power delivered or absorbed by different electrical elements.
What is a mesh in the context of electrical networks?
-A mesh is a loop in an electrical network that does not contain any other loops within it. It is characterized by having the same first and last node.
How does mesh analysis help in obtaining the values of unknown currents?
-Mesh analysis provides a systematic approach to set up equations based on Kirchhoff's Voltage Law (KVL) for each mesh, which when solved, yield the values of the unknown currents flowing through the network.
What are the steps involved in performing mesh analysis?
-The steps involved in performing mesh analysis are: 1) Identify the total number of meshes in the network, 2) Assign mesh currents to each mesh, 3) Develop KVL equations for each mesh, and 4) Solve the KVL equations to find the mesh currents.
Why is mesh analysis only applicable to planar networks?
-Mesh analysis is only applicable to planar networks because it relies on the ability to draw the network without any branches crossing each other. Non-planar networks, where branches cross, cannot be analyzed using mesh analysis due to the complexity introduced by the crossings.
Can the direction of mesh current be chosen arbitrarily?
-Yes, the direction of mesh current can be chosen arbitrarily, but it is conventionally chosen as clockwise for convenience and to align with the typical current flow from the source on the left in the network.
What is the relationship between the number of meshes and the number of equations required in mesh analysis?
-The number of equations required to solve an electrical network using mesh analysis is equal to the number of meshes, which can be calculated using the formula: number of meshes = number of branches - number of nodes + 1.
How do you handle the situation where multiple mesh currents pass through the same resistor?
-When multiple mesh currents pass through the same resistor, the net current through the resistor is represented as the difference of the mesh currents, with the priority given to the mesh current for which the KVL equation is being written.
What is the significance of assigning clockwise direction to mesh currents?
-Assigning a clockwise direction to mesh currents is significant because it typically aligns with the direction of current flow from the source, which helps in obtaining positive values for the currents and simplifies the analysis.
How can mesh analysis be used to calculate power loss in a resistor?
-Once the mesh currents are determined through mesh analysis, the power loss in a resistor can be calculated using the formula: power loss = (current^2) * resistance, where 'current' is the current flowing through the resistor.
Outlines
🔍 Introduction to Mesh Analysis
The paragraph introduces mesh analysis as a method for analyzing electrical networks. It emphasizes the importance of understanding mesh analysis for determining the power delivered or absorbed by different electrical elements. The concept of a mesh is explained as a loop without any inner loops, and the steps for performing mesh analysis are outlined: identifying the number of meshes, assigning mesh currents, developing KVL equations for each mesh, and solving these equations. The paragraph also highlights that mesh analysis is only applicable to planar networks where no branch crosses another.
🧭 Assigning Mesh Currents and Developing KVL Equations
This paragraph delves into the specifics of assigning mesh currents, with a preference for the clockwise direction due to its convenience and alignment with the conventional current flow from the source. It explains the relationship between the number of meshes, branches, and nodes in a network, providing a formula to calculate the number of meshes. The process of developing KVL equations for each mesh is discussed, with an example illustrating how to account for the net current through shared resistors by prioritizing the mesh current of the mesh being analyzed.
🔧 Solving KVL Equations and Calculating Power Loss
The final paragraph demonstrates the application of mesh analysis through an example. It shows how to develop KVL equations for two meshes, taking care to prioritize the mesh current for the mesh being analyzed. The equations are then solved to find the mesh currents, and the power loss in a resistor is calculated using the current through it. The paragraph concludes with a summary of the key points to remember, such as considering the mesh current as the largest when drawing KVL equations, and emphasizes that more examples will be solved in future lectures for better clarity.
Mindmap
Keywords
💡Mesh Analysis
💡Kirchhoff's Voltage Law (KVL)
💡Mesh Current
💡Planar Network
💡Loop
💡Voltage
💡Current
💡Ohm's Law
💡Power
💡Resistor
Highlights
Mesh analysis is used to determine unknown currents in electrical networks.
The main aim of analyzing an electrical network is to obtain power delivered or absorbed by different elements.
Mesh is defined as a loop without any inner loops.
Mesh analysis involves identifying the total number of meshes in a network.
Each mesh is assigned a mesh current that flows only around the perimeter of the mesh.
KVL equations are developed for each mesh to find the mesh currents.
Mesh analysis is applicable only for planar networks where no branch crosses another.
The direction of mesh current can be chosen as clockwise or anticlockwise, but clockwise is preferred.
The number of equations required for mesh analysis equals the number of meshes, which is calculated as the branch number minus node number minus one.
An example problem demonstrates how to identify meshes, assign currents, develop KVL equations, and solve for mesh currents.
The outer loop of a network is not considered a mesh if it contains inner loops.
When developing KVL equations, the net current through a shared resistor is the difference between the mesh currents.
The priority is given to the mesh current of the mesh for which the KVL equation is being written.
Solving the KVL equations yields the mesh currents, which can be used to calculate power loss in resistors.
The power dissipated in a resistor is calculated as the square of the current through it times the resistance.
Mesh analysis provides a systematic approach to solving complex electrical network problems.
Transcripts
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]
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