## What is KVL?

KVL stands for Kirchhoff voltage law. KVL states that the total voltage drops around the loop in any closed electric circuit is equal to the sum of total voltage drop in the same closed loop.

## What is KCL?

KCL stands for Kirchhoff current law. KCL states that all the incoming currents are equal to the total outgoing current in an electric circuit.

## What is Kirchhoff’s current law?

To solve a complex electric circuit, Kirchhoff provides two basic laws and theorems for the voltage and current in a given electric circuit. One law deals with the current flowing in an electric circuit, whereas another law deals with the voltage in a circuit.

If there is more than one resistance in an electric circuit, we can quickly solve it by using ohm's law. In a complex electric circuit with resistances, various other elements and branches make solving the circuit difficult. To make it easier, we need some set of current and voltage laws that help to obtain the equations of current and voltages; therefore, for this purpose, we can use Kirchhoff's current law.

KCL is also known as the current law, which states that the currents entering the junction will be precisely equal to the outgoing current or current leaving the junction. In other words, the total of all the currents entering or leaving a junction in an electric circuit will be equal to zero. The current law was given by Kirchhoff given an idea of conservation of electric charges.

Assume a junction shown in the circuit below.

Assume currents ${I}_{1},{I}_{2}$ as incoming current or the currents entering the junction and take an as positive while ${I}_{3},{I}_{4},{I}_{5}$ as outgoing current or the currents leaving the junction and take outgoing current as negative.

The current equation can be written as shown below.

${I}_{1}+{I}_{2}+{I}_{3}+{I}_{4}+{I}_{5}...=0$

## What is the DC circuit term?

- Circuit - circuit is a means of operating a closed loop in which a current flows.
- Line - one line of connecting objects or assets.
- Node - node is a junction, a connection, or terminal within a circuit with two or more circuit components connected that provide a point of connection between branches or more. The point or the junction where one or more branches of an electric circuit meet is termed as a node. For current to flow in an electric circuit the circuit should be a closed circuit. The node is indicated by a dot.
- Branch - a department or collection of additives that are related to dissertations or related feeds between nodes.
- Loop - a simple closed method in a circuit where no circuit information or node is encountered more than once.
- Mesh - series of single closed loop lines that do not include alternatives. There are no loops inside the mesh.

## History of Kirchhoff's circuit law

The set of rules that deals with calculation of voltages and currents to converse the electrical energy was developed by German physicist Gustav Kirchhoff in 1845. Also, KVL and KCL are collectively known as Kirchhoff's circuit law.

These rules can be applied to time and frequency domains and form the basis for network analysis. Kirchhoff's laws can be understood as the coincidence of Maxwell's calculations in the lower frequency range. They are accurate in DC circuits and in AC circuits in frequencies where the wavelength of the electromagnetic wave is very large compared to circuits.

## Kirchhoff voltage law?

KVL is also known as voltage law which states that in any given electric circuit, the algebraic sum of all the voltages is equal to zero. In other words, the voltages present in a circuit are equal to the voltage drops present in the same circuit. Kirchhoff voltage law deals with the conservation of energy.

## How to use KVL?

Assume any electric closed circuit and start from any point in one direction and note all the voltages drop either positive or negative. Take care that it is important to maintain any one direction either positive or negative. KVL helps to solve any complex network by providing its voltage equation.

Assume a junction shown in the circuit below.

Therefore, when applying Kirchhoff's electronics law to a particular circuit, it is crucial to pay special attention to the algebraic signals (+ and -) of power outages in all aspects and the sources of the sources; otherwise, our calculations may be incorrect.

The voltage equation can be written as shown below.

${V}_{1}+{V}_{2}+{V}_{3}+{V}_{4}=0$

## Terminologies in an electric network

- A closed-loop that provides a path to an electric current to flow is known as a circuit.
- One or more electric components connected between two nodes is termed as a branch.
- A closed path in which no node is considered more than once is termed as the loop.
- A closed-loop that does not contain any other path is termed a mesh.

## Application of current law and voltage law

The procedure for applying current law and voltage law is as follows:

- Note the values of voltages, resistances, inductance given in the question.
- Assign a branch current for each branch or mesh.
- Find the KCL equation for each node.
- Find the KVL equation for each closed loop.
- Solve KVL and KCL equations with the help of a simultaneous linear equation and find the values of each branch current.
- Both are used in electromotive force, op-amp, and magnetic field topics.

## Common Mistakes

- When the same current passes through all the components then the connection is termed as the series connection.
- When components have the same voltage across them then it will be termed as the parallel connection.
- While obtaining voltage equations using the Kirchhoff voltage law, it is important to take the equation. Either use clockwise direction or choose anticlockwise equation.
- Always take care of calculations and write the number of the node for which equations you are providing.

## Context and Applications

This subject matter is tremendous inside the expert exam for each undergraduate and graduate publication, mainly for:

- Bachelor of Technology in the electrical and electronic department
- Bachelor of Science in Physics
- Master of Science in Physics

## Related Concepts

- Ohms law
- Conservation of charge
- Conservation of energy
- Simultaneous linear equation
- Thevenin law
- MOSFET

## Practice Problem

**Question-1** The algebraic sum of voltages in a closed loop is equal to ______.

(a) Infinite

(b) Zero

(c) One

(d) Five

**Correct answer: **(b)

**Explanation: **The algebraic sum of all the voltage drops in a circuit equal to zero.

**Question-2** Assume entering currents be ${I}_{1}=10\mathrm{A}$, ${I}_{2}=15\mathrm{A}$, ${I}_{3}=20\mathrm{A}$ and leaving currents be ${I}_{4}=25\mathrm{A}$, ${I}_{5}=5\mathrm{A}$ and ${I}_{6}$. Find ${I}_{6}$.

(a) 10A

(b) 28A

(c) 15A

(d) 16A

**Correct answer: **(c)

**Explanation: **According to KCL, entering currents will be equal to leaving currents.

$10+15+20=25+5+{I}_{6}\phantom{\rule{0ex}{0ex}}{I}_{6}+30=45\phantom{\rule{0ex}{0ex}}{I}_{6}=15\mathrm{A}$

**Question-3 **KVL deals with_____.

(a) Conservation of charge

(b) Conservation of energy

(c) Both a and b

(d) None of these

**Correct answer: (**b)

**Explanation:** The algebraic sum of all the voltage drops in a circuit equal to zero.

**Question-4** The basic law for analyzing electric networks is ____.

(a) Ohms law

(b) Faraday law

(c) Newton law

(d) Kirchhoff's law

**Correct answer: **(d)

**Explanation:** Kirchhoff's current law is used to solve the complex circuit element by providing current and voltage equations.

**Question-5 **According to KCL, for the given network, what will be the correct current equation?

(a) ${I}_{1}={I}_{2}+{I}_{3}+{I}_{4}-{I}_{5}$

(b) ${I}_{1}+{I}_{3}+{I}_{5}={I}_{2}+{I}_{4}$

(c) ${I}_{2}+{I}_{5}={I}_{1}+{I}_{3}-{I}_{4}$

(d) ${I}_{4}+{I}_{5}-{I}_{2}={I}_{1}-{I}_{3}$

**Correct answer: **(b)

**Explanation:** According to KCL, the total current entering the junction will be equal to the current leaving the junction.

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