<< Chapter < Page Chapter >> Page >

Kirchhoff's current law

At every node, the sum of all currents entering or leaving a node must equal zero. What this law means physically is that chargecannot accumulate in a node; what goes in must come out. In the example, [link] , below we have a three-node circuit and thus have three KCLequations. i i 1 0 i 1 i 2 0 i i 2 0 Note that the current entering a node is the negative of the current leaving the node.

Given any two of these KCL equations, we can find the other by adding or subtracting them. Thus, one of them is redundantand, in mathematical terms, we can discard any one of them. The convention is to discard the equation for the(unlabeled) node at the bottom of the circuit.

The circuit shown is perhaps the simplest circuit that performs a signal processing function. The input is providedby the voltage source v in and the output is the voltage v out across the resistor labelled R 2 .

In writing KCL equations, you will find that in an n -node circuit, exactly one of them is always redundant. Can you sketch a proof of whythis might be true? Hint: It has to do with the fact that charge won't accumulate in one place on its own.

KCL says that the sum of currents entering or leaving a node must be zero. If we consider two nodes together as a"supernode", KCL applies as well to currents entering the combination. Since no currents enter an entire circuit,the sum of currents must be zero. If we had a two-node circuit, the KCL equation of one must be the negative of the other, We can combine all but one node in a circuit into a supernode; KCL for the supernodemust be the negative of the remaining node's KCL equation. Consequently, specifying n 1 KCL equations always specifies the remaining one.

Got questions? Get instant answers now!

Kirchhoff's voltage law (kvl)

The voltage law says that the sum of voltages around every closed loop in the circuit must equal zero. A closed loop hasthe obvious definition: Starting at a node, trace a path through the circuit that returns you to the origin node. KVLexpresses the fact that electric fields are conservative: The total work performed in moving a test charge around a closedpath is zero. The KVL equation for our circuit is v 1 v 2 v 0 In writing KVL equations, we follow the convention that an element's voltage enters with a plus sign when traversing theclosed path, we go from the positive to the negative of the voltage's definition.

For the example circuit , we have three v-i relations, two KCL equations, and one KVL equation for solving for the circuit's six voltages andcurrents. v-i: v v in v 1 R 1 i 1 v out R 2 i out KCL: i i 1 0 i 1 i out 0 KVL: v v 1 v out 0 We have exactly the right number of equations! Eventually, we will discover shortcuts for solving circuit problems; for now,we want to eliminate all the variables but v out and determine how it depends on v in and on resistor values. The KVL equation can be rewritten as v in v 1 v out . Substituting into it the resistor's v-i relation, we have v in R 1 i 1 R 2 i out . Yes, we temporarily eliminate the quantity we seek. Though notobvious, it is the simplest way to solve the equations. One of the KCL equations says i 1 i out , which means that v in R 1 i out R 2 i out R 1 R 2 i out . Solving for the current in the output resistor, we have i out v in R 1 R 2 . We have now solved the circuit : We have expressed one voltage or current in terms of sources andcircuit-element values. To find any other circuit quantities, we can back substitute this answer into our original equations orones we developed along the way. Using the v-i relation for the output resistor, we obtain the quantity we seek. v out R 2 R 1 R 2 v in

Referring back to [link] , a circuit should serve some useful purpose. What kind ofsystem does our circuit realize and, in terms of element values, what are the system's parameter(s)?

The circuit serves as an amplifier having a gain of R 2 R 1 R 2 .

Got questions? Get instant answers now!

Questions & Answers

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of electrical engineering i' conversation and receive update notifications?

Ask