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Kirchhoff’s circuit laws are facilitating rules for analyzing electrical circuits. These rules are handy where circuits are more complex beyond the scope of series and parallel combination of resistances and where circuits involve intermixing of electrical sources and resistances (appliances or resistors). Kirchhoff’s laws are brilliant reflection of fundamental laws like conservation of charge and energy in the context of electrical circuits.

There are two Kirchhoff’s laws which are known by different names :

1: Kirchhoff’s current law (KCL) : It is also referred as Junction or point or Kirchhoff’s first rule.

2: Kirchhoff’s voltage law (KVL) : It is also referred as Loop or Mesh or Kirchhoff’s second rule.

Kirchhoff’s current law (kcl)

No point in the circuit accumulates charge. This is the basic consideration here. Then, the principle of conservation of charge implies that the amount of current flowing towards a point should be equal to the amount of current flowing away from that point. In other words, net current at a point in the circuit is zero. We follow the convention whereby incoming current is treated as positive and outgoing current as negative. Mathematically,

I = 0

There is one exception to this law. A point on a capacitor plate is a point of accumulation of charge.

Problem : Consider the network of resistors as shown here :

Network of resistors

Each resistor in the network has resistance R.

Each resistor in the network has resistance R. The EMF of battery is E having internal resistance r. If I be the current that flows into the network at point A, then find current in each resistor.

Solution :

It would be very difficult to reduce this network and obtain effective or equivalent resistance using theorems on series and parallel combination. Here, we shall use the property of symmetric distribution of current at each node and apply KCL. The current is equally distributed to the branches AB, AD and AK due to symmetry of each branch meeting at A. We should be very careful about symmetry. The mere fact that resistors in each of three arms are equal is not sufficient. Consider branch AB. The end point B is connected to a network BCML, which in turn is connected to other networks. In this case, however, the branch like AK is also connected to exactly similar networks. Thus, we deduce that current is equally split in three parts at the node A. If I be the current entering the network at A, then applying KCL :

Current flowing away from A = Current flowing towards A

As currents are equal in three branches, each of them is equal to one-third of current entering the circuit at A :

I A B = I A D = I A K = I 3

Currents are split at other nodes like B, D and K symmetrically. Applying KCL at all these nodes, we have :

I B C = I B L = I D C = I D N = I K N = I K L = I 6

Network of resistors

Current in resistors

On the other hand, currents recombine at points C, L, N and M. Applying KCL at C,L and N, we have :

I L M = I C M = I N M = I 3

These three currents regroup at M and finally current I emerges from the network.

Kirchoff’s voltage law (kvl)

This law is based on conservation of energy. Sum of potential difference (drop or gain) in a closed circuit is zero. It follows from the fact that if we start from a point and travel along the closed path to the same point, then the potential difference is zero. Recall that electrical work done in carrying electrical charge in a closed path is zero and hence potential difference is also zero :

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
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what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Electricity and magnetism. OpenStax CNX. Oct 20, 2009 Download for free at http://cnx.org/content/col10909/1.13
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