Advertisement

## Kirchhoff's first law , Kirchhoff's second law & how to solve problems of Kirchhoff's laws

**Kirchhoffs Laws**

**Some electric circuits consists of many branches and are too complicated to be managed by Ohms law because the electric current passing through them is different in each branch , For such cases a German scientist called Kirchhoff set two relations called Kirchhoffs laws which enable one to analyze arbitrary circuits . **

**Kirchhoffs first law : based on conservation of electric charge**

**The electric current through a metallic conductor is a stream of negative free electrons ( electric charges ) flowing from one point to another , ****These charges do not accumulate at any point in the circuit but they move through the circuit continuously & the conductor is not charged during the flow of the electric current .**

**According to this Kirchhoff has deduced that the sum of charges flowing into the node is equal to the sum of charges flowing out of that node and formulated his first lawKirchhoffs current lawas follows : **

**Kirchhoffs first law : At any node ( junction ) in an electrical circuit , the sum of currents flowing into the node is the sum of currents flowing out of that node , or the algebraic sum of the electric currents at a point ( a node ) in a closed circuit equals zero .**

**The mathematical relation for Kirchhoffs first law**

**Sum of currents flowing into point ( A ) = Sum of currents flowing out of point ( A ) **

** I _{(in)}** =

**I**

_{(out )}**At the junction ( node ) , The current flowing into the point and that flowing out of it have positive sign ( + ) .**

**I _{1} + I_{2} = I_{3} + I_{4}**

**The algebraic sum of currents at junction in a closed circuit = zero**

** I = 0**

**At the junction ( node ) , The current flowing into the point has positive sign ( + ) ,The current flowing out of the point has negative sign ( ) .**

**I _{1} + I_{2}I_{3}I_{4} = 0**

**Kirchhoffs first law is used in the circuits that include resistors connected in parallel due to the presence of junctions for currents distribution .**

**Kirchhoffs first law is an application of the law of conservation of charge ( the quantity of charge flowing into a node is equal to the quantity of charge flowing out of that node ) because the electric current intensity in ( Amperes ) equals the quantity of electric charges in ( Coulomb ) crossing a cross- section area in one second .
**

**Kirchhoffs second law : based on conservation of energy **

**Potential difference ( V ) expresses the work done or the energy required to transfer a unit electric charge across a component in the circuit , It is measured in Volt , It is calculated from the relation : V = I R , Where : R is the resistance of the part in the circuit at which the potential difference is required to be calculated at its ends .**

**Electromotive force ( V _{B} ) expresses the work done or the energy required to transfer a unit electric charge once round the whole circuit , It is measured in Volt , It is calculated from the relation :V_{B} = I ( R + r ) , Where : ( R ) is the total external resistance , ( r ) is the internal resistance of the source .**

**This is formulated by Kirchhoff in his second law ( Kirchhoffs voltage law ) as follows :**

**The mathematical relation for Kirchhoffs second law**

**How to solve problems of Kirchhoffs laws **

Advertisement