Kirchhoff’s Voltage Law and Kirchhoff’s Current Law
In this article, we will explore Kirchhoff’s Voltage Law and Kirchhoff’s Current Law in detail, delving into their principles and applications. We will examine how these laws form the foundation of circuit analysis, providing a solid framework for understanding the behavior of electrical networks. By grasping the concepts and techniques associated with KVL and KCL, readers will gain valuable insights into electrical circuit analysis and be equipped with powerful tools for solving complex electrical problems.
Kirchoffs’ Current law (KCL)
Consider a junction point. The figure shows the complex network. At this junction point, if I1=2A, I2=4A, and I3=1A, then to find the current I4, we say the sum of current inflowing is 4+4=8A whereas the sum of current flowing away from the circuit is 2+I4 A.
Thus I4 = 6A.
This study of currents flowing in and out in the circuit is nothing but the use of Kirchhoff’s Current Law. This KCL (Kirchhoff’s law) can be stated as,
The sum of current flowing towards a junction equals the sum of current flowing away from the junction.
This law can also be stated as,
The algebraic sum of all the currents meeting at point O is always zero. The letter algebraic means in view of the signs of various currents.
ΣI at junction point O = 0
The above figure shows that currents I1 and I2 are positive, while I3 and I4 are negative.
Applying KCL, ΣI at junction point O = 0
I1 +I2-I3-I4 = 0
Ie. I1 + I2 = I3 + I4
Kirchhoff’s law is very useful in network simplification.
Kirchoff’s Voltage Law [KVL]:
In any of the networks, the algebraic sum of voltage drops across the circuit elements of any closed circuit is equal to the algebraic sum of all the branch voltages around any closed circuit or closed loop is always zero.
Around a closed path Σv=0
The law states that if one starts at a definite point of a closed path and goes on tracing and noting all the potential changes (either drops or rises) in any one particular direction till the starting point is reached again, he must be at the same potential with which he started tracing a closed path.
The sum of all the potential risks must equal the sum of all the potential drops while tracing any closed circuit path. The total change in potential along a closed way is always zero.
This law is very useful in the loop analysis of the network.
Sign Conventions to be followed while Applying KVL
The voltage drop occurs across the resistance whenever a current flows through the resistance. The polarity of this voltage drop always depends on the direction of the current. The current always flows from higher to lower potential.
In Fig-(a), current I am flowing from right to left. Therefore, point B is a higher potential than point A, as shown in Fig.
In Fig-(b), current I flow from left to right. Thus point A is at a higher potential than point B, which is also shown.
Once all such polarities are marked in the given circuit, we can apply KVL to any closed path in the circuit.
Now while tracing a closed path, if we go from the -ve marked terminal to the +ve marked terminal, that voltage must be taken as positive. This is called potential rise.
For example, if branch AB is traced from A to B, the drop across it must be considered a rise and taken as +IR while writing the equations.
While tracing a closed path, if we go from the +ve marked terminal to the -ve marked terminal, that voltage must be taken as negative. This is called the potential drop.
For example, in Fig-(a) only, if the branch is traced from B to A, it should be taken as negative, as -IR, while writing the equations.
Similarly, in Fig-(b), if the branch is traced from A to B, there is a voltage drop, and the term must be negative as -IR while writing the equation. U the branch is traced from B to A, it becomes a rise in voltage, and the term must be written positive as +IR while writing the equation.
In Fig-(b), current I flow from left to right. Hence point A is at a higher potential than point B, as shown.
