# What is Kirchhoff's Law and Its Use

0

## What is Kirchhoff's Law ?

Kirchhoff's laws refer to two fundamental principles in electrical circuit theory that describe the behavior of electric circuits.

## Kirchhoff's Current Law (KCL):

Kirchhoff's Current Law (KCL) states that the total amount of electric current flowing into a point in a circuit is equal to the total amount of current flowing out of that same point.

Explain: Total electric charge entering a junction must equal the total electric charge leaving the junction, as electric charge is conserved in a closed system. Therefore, the sum of all the currents entering in a junction must be equal to the sum of all the currents leaving that junction.

Mathematically, KCL can be expressed as:

### ∑I_in = ∑I_out

where, ∑I_in is the algebraic sum of all currents flowing into the junction and ∑I_out is the algebraic sum of all currents flowing out of the junction.

#### Example:

I1 →          I2 →
┌───●───┐     ┌───●───┐
│   │   │     │   │   │
R1   R2   R3    R4  R5  RL
│   │   │     │   │   │
└───●───┘     └───●───┘
I3 →

The current flowing through each branch is represented by I1, I2, and I3, and the resistors in the circuit are labeled as R1, R2, R3, R4, R5, and RL. The load resistor RL represents the device or component that consumes power from the circuit.

To apply KCL, let's consider the current flowing into the junction at the top of the circuit. According to KCL, the sum of the currents entering the junction must be equal to the sum of the currents leaving the junction.

Let's assume that I1 = 2 A, I2 = 3 A, and I3 = 1 A. To find the current flowing through the load resistor RL, we need to apply KCL as follows:

∑I_in = ∑I_out

I1 + I2 + I3 = IL

2 A + 3 A + 1 A = IL

Simplifying the equation, we get:

IL = 6 A

## Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law (KVL) states that the sum of all the voltages in a closed loop of a circuit must equal zero.

Explain: Sum of all the voltage drops across the resistors and other components in a closed loop in a circuit must equal the total voltage supplied by the voltage sources in that loop, as energy is conserved in a closed system.

Mathematically, KVL can be expressed as:

### ∑V = 0

where, ∑V is the algebraic sum of all the voltage drops in a closed loop in the circuit.

#### Example:

Consider a simple circuit consisting of a voltage source V1 and two resistors R1 and R2, as shown below:

+-----R1-----+
|             |
V1 ---+             +---R2---+
|             |        |
+---------------------+

To apply KVL, we can choose a closed loop in the circuit and follow it in a clockwise or counterclockwise direction. Let's choose the loop shown in red in the figure above, starting at point A:

Starting at point A, we encounter a voltage drop of V1 across resistor R1, and then another voltage drop of V_R2 = I_R2 * R2 across resistor R2, where I_R2 is the current flowing through resistor R2.

Since the loop is closed, the sum of all the voltage drops must be equal to the sum of all the voltage sources, and we can write:

V1 - V_R2 = 0

We can use Ohm's Law to express I_R2 in terms of the resistance and voltage, and substitute into the equation:

V1 - (V_R2 / R2) * R2 = 0

Simplifying the equation, we get:

V1 - V_R2 = 0

Therefore, this is an application of Kirchhoff's Voltage Law (KVL) for the chosen closed loop in the circuit.

## Use Of Kirchhoff's Law

Kirchhoff's laws are fundamental principles in the field of electrical engineering and are used to analyze and solve complex circuits.

• Kirchhoff's Current Law (KCL) is used to analyze circuits with multiple current paths and junctions. It helps in calculating the current flowing through each branch and junction of the circuit. Engineers use KCL to design and troubleshoot complex electrical circuits in various applications, such as power generation, transmission, and distribution systems, electronic devices, and control systems.
• Kirchhoff's Voltage Law (KVL) is used to analyze circuits with multiple voltage sources and loops. It helps in calculating the voltage drops across each component in the circuit. Engineers use KVL to design and troubleshoot complex electrical circuits in various applications, such as signal processing, communication systems, and control systems.

Overall, Kirchhoff's laws are essential tools for electrical engineers to understand and analyze complex circuits. They provide a systematic and rigorous method for calculating currents and voltages in complex circuits, which is critical in designing and troubleshooting electrical systems.