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Circuit Analysis Using Kirchoff Current Law (KCL) and Kirchoff Voltage Law KVL

Why are the 2 Laws required?

Simple circuits can be analyzed by using Ohms Law. i.e. Using knowledge of Ohm's law, we can find out the current and potential differences across the Resistances. But this is possible only for Simple circuits.

What if the circuits get complicated? 

e.g. there are multiple Voltage Sources, i.e. Batteries. Also, the circuit can be made complex by adding resistances in such a manner that one is not able to figure out if the Resistances are in Parallel and Series. Under such complex scenarios, the circuit is not easy to analyze, i.e. one cannot find the Potential difference and current in the circuit for the identified Resistances. To make life easy; Kirchoff came out with 2 Laws for analyzing the complex circuits. These laws are known as Kirchoff's Current Law (KCL) and Kirchoff Voltage Law (KVL), respectively.

Kirchoff Current Law is based on the Law of Conservation of Charge

Kirchoff Voltage Law is based on the Law of Conservation of Energy

State the Kirchoff's Law (This question is asked in CBSE Board exam followed by a Circuit Analysis Question)

Kirchhoff's junction rule: the total current coming into any junction must equal the total current coming out of the junction. The Algebraic sum of current entering a Junction is equal to the sum of currents entering the loop.

Kirchhoff's Voltage rule: the sum of the voltages around any closed loop must add up to zero. This is the based on the idea that if traverse a loop in a complex circuit then the starting point and the end point is same. There should not be any potential difference between the same point on the circuit. The Algebraic sum of voltage differences due to Resistance and Batteries should be 0. 

Method for Applying KVL and KCL for Circuit Analysis

KVL- If the loop is being traversed, then the following needs are done: -

First take a closed-loop (Generally we have 2 or 3 Loops in CBSE Numerical) and show an anti-clockwise or clockwise arrow in the loop, Preferably select the Loop direction in a manner that when battery comes in the loop; battery potential is rising from Negative to Positive for a battery, so the Voltage will be positive while moving through the loop. Select the loops with Maximum of Batteries included in them

Within the loop if the assumed Current direction and the assumed Direction of Loop (clockwise or anti clockwise) is same then the Potential Difference would be falling across a Resistance i.e. take the potential difference (I*R) to be negative but if the Direction of Current and assumed Direction of Loop are not same then please take I*R to be negative.

Sometimes we may have to include a Loop which contains elements such as batteries and resistors already used in another loop. Such Loops are called as Meshes. So a loop can be a Mesh, but a Mesh cannot be a Loop

KCL- Select the Major Nodes/Junctions in the circuit and apply the KCL to these Major Nodes. Major nodes have maximum Branches connecting to them.

What is a Loop in KVL

A loop is any closed path through the circuit which encounters no node more than once.

what is a Node?  – any point where 2 or more circuit elements are connected

Wires usually have negligible resistance

Each node has one voltage (w.r.t. ground)

 Branch – a circuit element between two nodes

Junction - any point where 3 or more circuit elements are connected

With the help of KCL and KVL (Algebraic additions of current and Potential Differences), one can get few independent equations containing Unknows assumed in the circuit. The aim should be to create three equations and solve them to get currents in various branches,

Generally, in a complex circuit Number of Branches > Number of Junctions> Number of Loops>Number of Meshes

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