7. Kirchhoff Current Law ( KCL ) - Theory, Sign Conventions, Example Problem |BEE|
Summary
TLDRIn this educational video, the host explains the concept of Kirchhoff's Current Law (KCL), which states that the algebraic sum of currents at a junction is zero. They use a simple circuit diagram to demonstrate how to apply KCL to find unknown currents, emphasizing the importance of understanding incoming and outgoing current directions. The video also offers tips for solving more complex circuits, highlighting the need to identify junctions and form equations accordingly.
Takeaways
- 😀 The video discusses Kof's current law, also known as SKCL, which states that the algebraic sum of electric currents meeting at a junction is equal to zero.
- 🔌 A junction is defined as a point where three or more branches meet, and branches are parts of a circuit.
- 📈 Incoming currents at a junction are considered positive, while outgoing currents are considered negative.
- 🔄 The KCL can be referred to as the conservation of charge, emphasizing the balance of currents at a junction.
- 📚 The video provides an example to illustrate how to apply KCL in a circuit, involving currents labeled as i1, i2, i3, i4, and i5.
- 🔢 In the example, the KCL equation is formed by considering the sum of incoming currents (i1, i3, i4) equal to the sum of outgoing currents (i2, i5).
- 🔍 The video solves three sub-questions based on the circuit diagram, finding values for ix, iy, and iz under different conditions.
- 🤔 The video explains that in complex networks, you must identify all junctions, assume initial voltages, and form KCL equations for each junction.
- 🔋 The video mentions that in complex circuits, voltages and resistances will be involved, and Ohm's Law (V = IR) can be used to solve for currents and resistances.
- 📘 The video concludes by encouraging viewers to watch more videos on the channel for further understanding of complex circuits and the application of KCL.
Q & A
What is the main principle of Kirchhoff's Current Law (KCL)?
-Kirchhoff's Current Law states that the algebraic sum of the electric currents meeting at a junction or node is equal to zero. This means that the sum of incoming currents is equal to the sum of outgoing currents at any given node.
What is a junction in the context of electrical circuits?
-A junction is a point in an electrical circuit where three or more branches meet. It is the location where currents can either enter or leave the junction.
How are incoming and outgoing currents treated in KCL?
-In KCL, incoming currents are considered as positive, while outgoing currents are considered as negative. This helps in setting up the algebraic sum to zero for the currents meeting at a junction.
Can you explain the concept of conservation of charge in relation to KCL?
-The conservation of charge is a fundamental principle that states the total charge in an isolated system remains constant over time. In the context of KCL, this principle is reflected in the fact that the sum of currents at a junction must be zero, indicating that charge is neither created nor destroyed, just transferred between branches.
What is the significance of the direction of current in applying KCL?
-The direction of current is significant when applying KCL because it determines whether a current is considered incoming (positive) or outgoing (negative). If the direction is not given, it must be assumed for the purpose of setting up the KCL equations.
In the given example, how is the KCL equation set up for the circuit diagram?
-In the example, the KCL equation is set up by identifying the incoming and outgoing currents at the junction. The equation is formed by summing the incoming currents (5 amp, iZ, and iY) and setting it equal to the sum of the outgoing currents (IX and 3 amp).
What is the first condition given in the example for finding IX, and what is the result?
-The first condition given is when iY is equal to 5 amp and iZ is equal to 3 amp. Substituting these values into the KCL equation results in IX being equal to 10 amp.
How is the second condition in the example used to find the value of iY?
-The second condition states that IX is equal to 4 amp and iZ is equal to 4 times iY. By substituting these values into the KCL equation and solving for iY, it is found that iY equals 2 amp.
What does the third condition in the example tell us about the relationship between IX, iY, and iZ?
-The third condition states that IX is equal to iY, which is also equal to iZ. Using the KCL equation and substituting iZ for IX and iY, it is determined that iZ is equal to -2 amp, indicating that the current is flowing in the opposite direction.
What are some steps to follow when solving complex circuit problems using KCL?
-When solving complex circuits, one should first identify all junctions, assume initial voltages (VKN = 0), and unknown current directions. Then, form KCL equations for each junction. Remember sign conventions for adding or subtracting voltages, and use Ohm's Law (V = IR) to relate voltage, current, and resistance. These steps will help in solving for unknowns in more complicated circuits.
Outlines
📚 Introduction to Kirchhoff's Current Law (KCL)
This paragraph introduces the concept of Kirchhoff's Current Law (KCL), which is an essential principle in electrical circuit analysis. It explains that the algebraic sum of currents meeting at a junction or node equals zero, emphasizing the importance of understanding the terms 'junction' and 'branch'. The paragraph also illustrates how to apply KCL using an example with five currents (i1, i2, i3, i4, i5), where incoming currents are positive, and outgoing currents are negative. The example demonstrates the process of setting up and solving an equation based on KCL to find unknown currents in a circuit.
🔍 Applying KCL to Solve Circuit Problems
This paragraph continues the discussion on KCL by providing a practical example of a circuit diagram with three sub-questions to solve. It explains the process of identifying the junction and the currents entering and leaving it, using the law to set up equations for the currents (ix, iy, and iz). The paragraph demonstrates solving for ix when iy and iz are given, finding iy when ix and a multiple of iy are provided, and determining iz when ix, iy, and iz are all equal. It concludes with a reminder of the importance of understanding KCL for solving more complex circuits.
🛠️ Advanced Circuit Analysis Techniques
The final paragraph delves into the steps and conventions needed for analyzing more complex electrical circuits using KCL. It advises viewers to identify all junctions, assume initial voltages, and form KCL equations for each junction, even when current directions are not explicitly given. The paragraph also covers the rules for adding or subtracting voltages based on the connection of terminals and the fundamental principles of current flow from higher to lower potential. It wraps up with a mention of Ohm's Law and its variations, setting the stage for future videos that will tackle more complicated circuits and their analysis.
Mindmap
Keywords
💡Kirchhoff's Current Law (KCL)
💡Junction
💡Branch
Highlights
Introduction to the concept of Kirchhoff's Current Law (KCL).
Explanation that KCL states the algebraic sum of electric currents at a junction is zero.
Definition of a junction as a point where three or more branches meet.
Clarification that incoming currents are considered positive and outgoing currents are negative.
Introduction of an example to illustrate KCL with five currents meeting at a junction.
Equation setup for KCL: i1 + I3 + I4 = I2 + I5.
Description of a circuit diagram and the task to find currents ix, iy, and iz.
Application of KCL to a junction in a circuit diagram, balancing incoming and outgoing currents.
Solution for finding IX when iy equals 5A and iz equals 3A, resulting in IX = 10A.
Second condition: finding iy if IX equals 4A and iz equals 4 times iy, leading to iy = 2A.
Third condition: finding iz if IX equals iy equals iz, resulting in iz = -2A.
Discussion on solving complex networks using KCL, emphasizing the importance of identifying junctions.
Instructions on assuming initial voltage VKN equal to zero and unknown current direction.
Explanation of sign conventions for adding or subtracting voltages based on connection polarity.
Introduction of Ohm's Law (V = IR) and its implications for solving complex circuits.
Promise of future videos explaining how to apply KCL in more complex circuits.
Invitation for viewers to ask questions in the comments and request more videos.
Transcripts
[Music]
hello everyone welcome back to my
YouTube channel trouble free in today's
video we are going to learn about the
kof's current law in the previous video
I explained about the kof's voltage law
which is nothing but the kvl and it's
related examples now let us learn the
kof's current law uh which is in short
called skcl along with an example so
that you will understand it more better
so first what does this K off's current
law say it says that the algebraic sum
of the electric currents meeting at a
junction or node is equal to zero okay
so first of all what do you mean by a
junction junction is nothing but it is a
point where three or more branches will
meet so what do you mean by Junction it
is a point where three or more branches
will meet what do you mean by Branch
this is called as a branch okay
so at at a particular Junction so this
is called as a junction here so at this
Junction whatever currents are meeting
their sum should be equal to zero okay
so whatever currents are coming into the
junction they are considered as positive
and whatever the currents are leaving
the junction that is the outgoing
currents they are considered as negative
okay and the KCl can also be called as
the conservation of charge don't worry
I'll explain you for example see what is
the direction here it is coming inside
the junction right so let us assume them
as
i1 I2 I3 I4 and I5 we have five currents
here so what does kof's current law say
algebraic sum of the electric currents
meeting at a junction or node is equal
to zero so all the sum of all these
currents should be equal to what Z so
sum of all these currents should be
equal to zero let us see how and what
did I say here incoming currents should
be considered as positive and the
outgoing currents should be considered
as negative right so here what are the
incoming currents i1 is the incoming
current so it is considered as positive
I2 is going outside
so minus I2 and next I3 again it is
coming inside so plus I3 again I4 is
also coming inside so plus I4 and I5 is
leaving the junction it is going outside
so minus I5 is equal
to0 you can also write this as i1 + I3 +
I4 is equal to I2 + I5 if you send the
two negative terms to the other side of
the equation you can write the equation
in this way also okay now um we have an
example also so so let us um try to
understand KC in a more better way by
using this example so this is the
circuit diagram we are having uh this is
a circuit diagram given this is the
given information and we have three uh
sub questions here we have to solve
those three sub questions okay so uh in
this circuit
diagram we have this is the junction
okay so this is the junction and to this
Junction this current is in Inc coming
this is outgoing again this is incoming
this is incoming this is outgoing right
so find iix iy and Iz you have to find
iix i y and I Z given some conditions
okay so first let us try to write
the um kof's current law equation let us
consider this as a junction a so
at
Junction a some of all the currents
should be equal to zero right or you can
also
write sum of incoming current should be
equal to sum of outgoing current right
that is what we wrote here right sum of
incoming currents is equal to sum of
outgoing currents so let us try to form
the equation here so here what are
incoming currents 5 amp is incoming
current and i z i z is also incoming
current iy is also incoming current here
IX is outgoing current and 3 amp is also
outgoing current so that is equal to iix
plus 3 amp okay now let us look at each
of the question and try to find out find
IX when iy is equal to 5 a and I Z is
equal to 3 amp so this is the main
equation that we got so taking the first
condition
and first
condition so what does the first
condition
says i y is equal to 5 and I Z is equal
to 3 let us substitute these values here
so it becomes 5 + i z is how much 3 plus
i y is how much 5 is equal to IX you
have to find plus three right so here
what will
happen
um wait give me a second yeah you're
good so 3 three will go so we will get
iix is equal to 10 amp okay 5 + 5 is 10
right so IX is equal to 10 amp given the
first condition now let us go for the
second condition find iy if IX is equal
to 4 amp and I Z is equal to uh 4 * of
iy this is our uh equation from The
Junction right so see the same equation
I wrote it here because uh we don't have
place here I just copied the same
equation over here now what is our
second
question find iy if IX is equal to 4 amp
and I Z is equal to 4 * of iy so what
are the conditions you have to find iy
given ixal 4 i z is = 4 * time of iy so
let us substitute the same things over
here 5 + what is i z 4 * of iy plus I Y
we don't know IX is how much 4 + 3 so 5
+ 5
iyal 7 so send this 5 to that side it
will become 5 i y = 7 - 5 which is 5 i y
= 2 that means iy is equal to how much
2x 5
okay next what is the third condition
find i z if IX is equal to i y is equal
to i z okay so what is the third
condition iix isal i y isal to i z and
you have to find out what i z so again
take the same
equation 5
+ i z + i y = IX + 3 so uh let us
substitute everything with i z because
all the three are equal we can take any
variable but since we have to find out I
Z let us keep it so 5 + i z + i z + i z
is equal to sorry + 3 so 5 + 2 i z is =
to i z + 3 so send this i z to this side
and 5 to this side what do you get 2 i z
- i z is = 3 - 5 that
means so what do you mean by - 2 Amp - 2
Amp is nothing but the current is
flowing in the opposite direction we can
assume okay so this is how you solve the
kof's current law problems so at a given
Junction sum of incoming current should
be equal to sum of outgoing current you
know the symbol right summation symbol
sum of incoming current should be equal
to sum of outgoing current okay just
this one logic you have to remember and
you can solve okay this is fine but all
the circuits will not be this simple
they will have voltages they will have
uh resistance uh they will have
everything so in that case how you have
to solve to solve those kind of problems
we have some set of rules I'll tell you
what are those rules so in case of a
complex Network you have to follow these
steps first you have to identify all the
Junctions so what do you mean by a
junction where three or more branches
will meet a point where it could be
voltages it could be resistance it could
be anything okay and every time you have
to assume the initial voltage V KN which
is equal to Zer okay and assume unknown
current direction and form the KCl
equations for each Junction sometimes
the current direction will not be given
see in this example the current
direction is clear clearly given this is
incoming this is outgoing this is
incoming clearly given but sometimes the
current direction will not be given in
that case you have to assume it okay
assume it and form the KCl equations for
each Junction next important sign
conventions that you have to remember is
if at all the positive terminal is
connected to the negative terminal then
you can add the voltages positive is
connected to negative that is if
opposite signs are connected you can add
the voltages suppose if the same signs
are connected to each other then you
have to subtract the voltage
got it you have to minus the voltages
simple and current will always flow from
higher potential to lower potential
higher voltage to lower voltage okay
next you know oh SL at V is equal to ir
and from this you can write I equal to V
by R and you can also write R is equal
to V by I so these things you have to
remember while solving some of the
complicated circuits in the next coming
videos I'll take up a complicated
circuit and I will explain you how we
can figure out uh how we can apply KCl
how we can find out currents voltages
resistors resistances using that
complicated circuit okay so you have to
remember all these rules in order to um
work it out okay so thanks for watching
the video till the end guys if you still
have any doubts just let me know in the
comment section I'll be happy to help
you out and let me know what other
videos you need from my channel thank
you
[Music]
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