A Brief Explanation on How Kirchhoff’s Laws WorkingIn the year 1845, Gustav Kirchhoff (German physicist) introduces a set of laws which deal with current and voltage in the electrical circuits. The Kirchhoff’s Laws are generally named as KCL (Kirchhoffs Current Law) and KVL (Kirchhoffs Voltage Law). The KVL states that the algebraic sum of the voltage at node in a closed circuit is equal to zero. The KCL law states that, in a closed circuit, the entering current at node is equal to the current leaving at the node. When we observe in the tutorial of resistors that a single equivalent resistance, (RT) can be found when multiple resistors are connected in series or parallel, these circuits obey Ohm’s law. But, in complex electrical circuits, we cannot use this law to calculate the voltage and current. For these kinds of calculations, we can use KVL and KCL.Kirchhoff’s lawsKirchhoff’s laws mainly deal with voltage and current in the electrical circuits. These laws can be understood as results of the Maxwell equations in the low frequency limit. They are perfect for DC and AC circuits at frequencies where the electromagnetic radiation wavelengths are very large when we compare with other circuits. Kirchhoff’s Circuit LawsThere are various relationships among voltages and currents of an electrical circuit. These relationships are determined by Kirchhoffs laws such as KVL and KCL. These laws are used to determine the impedance of the complex network or equivalent electrical resistance and the currents flowing in the several branches of the n/w.Kirchhoff Current LawKCL or Kirchhoffs current law or Kirchhoffs first law states that the total current in a closed circuit, the entering current at node is equal to the current leaving at the node or the algebraic sum of current at node in an electronic circuit is equal to zero.Kirchhoff’s Current LawIn the above diagram, the currents are denoted with a,b,c,d and e. According to the KCL law, the entering currents are a,b,c,d and the leaving currents are e and f with negative value. The equation can be written as a+b+c+d= e + f Generally in an electrical circuit, the term node refers to a junction or connection of multiple components or elements or current carrying lanes like components and cables. In a closed circuit, the current flow any in or out of a node lane must exist. This law is used to analyze parallel circuits.Kirchhoff Voltage LawKVL or Kirchhoff’s voltage law or Kirchhoffs second law states that, the algebraic sum of the voltage in a closed circuit is equal to zero or the algebraic sum of the voltage at node is equal to zero. Kirchhoff’s Voltage LawThis law deals with voltage. For instance, the above circuit is explained. A voltage source ‘a’ is connected with five passive components, namely b, c, d, e, f having voltage differences across them. Arithmetically, the voltage difference between these components add together because these components are connected in series. According to the KVL law, the voltage across the passive components in a circuit is always equal & opposite to the voltage source. Hence, the sum of the voltage differences across all the elements in a circuit is always zero. a+b+c+d+e+f=0Common DC Circuit Theory TermsThe common DC circuit consists of various theory terms areCircuit: A DC circuit is a closed loop conducting lane in which an electrical current flows Path: A single lane is used to connect the sources or elements Node: A node is a connection in a circuit where multiple elements are connected together, and it is denoted with a dot. Branch: a branch is a single or collection of elements which are connected between two nodes like resistors or a source Loop: A loop in a circuit is a closed path, where no circuit element or node is met more than once. Mesh: A mesh doesn’t contain any closed path, but it is a single open loop, and it does not contain any components inside a mesh.Example of Kirchhoff’s LawsBy using this circuit, we can calculate the flowing current in the resistor 40ΩExample Circuit for KVL and KCLThe above circuit consist of two nodes, namely A and B, three branches and two independent loops.Apply KCL to the above circuit, then we can get the following equations.At nodes A and B we can get the equationsI1+I2=I2 and I2 =I1+I2Using KVL, the equations we can get the following equationsFrom loop1: 10=R1 X I1+R2 X I2= 10I1+40I2 From loop2: 20=R2 X I2+R2 X I3= 20I2+40I3 From loop3: 10-20=10I1-20 I2The equation of I2 can rewrite asEquation1= 10=10I1+40 (I1+ I2) = 50 I1+40 I2 Equation 2= 20=20I2 +40 (I1+ I2) = 40 I1+60 I2Now we have two concurrent equations which can be reduced to give the values of I1 and I2Replacement of I1 in terms of I2 gives the value of I1= -0.143 Amps Replacement of I2 in terms of I1 gives the value of I2= +0.429 AmpsWe know the equation of I3 = I1 + I2The flow of current in resistor R3 is written as -0.143 + 0.429 = 0.286 Amps The voltage across the resistor R3 is written as: 0.286 x 40 = 11.44 voltsThe –ve sign for ‘I’ is the direction of the flow of current initially preferred was wrong, In fact, the 20 volt battery is charging the 10 volt battery.This is all about Kirchoff’s laws, which includes KVL and KCL. These laws are used to calculate the current and voltage in a linear circuit, and we can also use loop analysis to calculate the current in each loop. Furthermore, any queries regarding these laws, please give your valuable suggestions by commenting in the comment section below.Photo Credits:Kirchhoff’s laws by blogspotExample of Kirchoff’s Laws by electronics-tutorials Share This Post: Facebook Twitter Google+ LinkedIn Pinterest Post navigation ‹ Previous Online Shop for Electrical and Electronic Project Kits IndiaNext › Paper Battery Construction and Working Related Content What is a Spectrum Analyzer : Working & Its Applications What is a Discharge Lamp : Design & Its Working What is an Inductive Reactance : Definition, Unit and Formula What is Eddy Current Dynamometer : Construction & Its Working One CommentI try the question and my answers are I1=0.134A,I2=-0.238A and l3=-0.095A. thanks I need more demonstration so that I will understand its.ReplyAdd Comment Cancel replyComment:Name * Email * Website
I try the question and my answers are I1=0.134A,I2=-0.238A and l3=-0.095A. thanks I need more demonstration so that I will understand its.Reply