__Kirchhoff’s laws__

Kirchhoff’s law was introduced by a famous German physicist named chech Robert Kirchhoff in 1847. Kirchhoff’s law is used for the analysis of circuit. There are two laws in Kirchhoff law known as:-

**KVL(Kirchhoff’s current law)****KCL(Kirchhoff’s voltage law)**

**Kirchhoff’s current laws**:- Kirchoff’s current law states that the algebraic sum of currents entering a node is zero.

mathematically:-

N

∑ i_{k }=0

K=đ

where **N** is the number of branches connected to node and **i _{k}** is the

**kth**current entering in a node.

Consider the node o is shown in the figure:-

**I _{1}+(-i_{2})+i_{3}+i_{4}+(-i_{5})=0**

Since the currents **I _{1}+i_{3}+i_{4}=i_{2}+i_{5}**

From the above analysis KCL can also be explained as

**The sum of currents entering a node is equal to the sum of the currents leaving the node.**

__KIRCHOFF’S VOLTAGE LAWS__

Kirchhoff’s voltage law states that the algebraic sum of all voltage around a closed path is zero.

Mathematically:-

** M**

** ∑ v _{1}=0**

** I=1**

Where M is the number of voltages in the loop and v1 is the ith voltage. In the given circuit diagram the sign on each voltage is the polarity of terminal. We can start with any branch and go arounf the loop either clock-wise or counter-clockwise.

When we start with the voltage source and go clockwise around the loop as shown in fig. then,voltages would be **–V _{1}+V_{2}+V_{3}-v_{4}** and

**+V**for example as we reached branch 4,the negative terminal met first,hence we have

_{5}**–V**.

_{4}Therefore KVL yields **–v _{1}+v_{2}+v_{3}-v_{4}+V_{5}=0**

On rearranging the equation of Kirchhoff’s law:-

**V _{2}+v_{3}+v_{5}=v_{1}+v_{4}**

From the above analysis we conclude

**Sum of voltage drops=sum of voltage raise**

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