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Kirchhoff’s Laws

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Kirchhoff’s Laws are the basic laws used in electrostatics to solve complex circuit questions. Kirchhoff’s Laws were given by Gustav Robert Kirchhoff who was a famous German Physicist. He gave us two laws Kirchhoff’s Current Law and Kirchhoff’s Voltage Law which are discussed in this article.

These laws deal with the flow of current and the voltage applied in the complex circuit and provide a way to solve these complex circuits. In this article, we will learn about Kichhoff’s Current Law, Kirchhoff’s Voltage Law, their applications, examples, and others in detail.

History of Gustav Robert Kirchhoff

Gustav Robert Kirchhoff was a German physicist who was born in Prussia a state under German Empire on 12 March 1824. He gave his contribution to the field of electrical circuits, black body radiation, and spectroscopy. He was the one who coined the term ‘Black Body Radiation’. Kirchhoff’s Circuit Law is the combination of Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL) which were published in 1845 as part of his doctoral dissertation. 

The image added below shows the Gustav Robert Kirchhoff

Gustav Robert Kirchhoff

 

Circuit analysis is carried out using these laws. They are helpful in the calculation of current flow and voltage flow in various streams across the network.

Kirchhoff’s Laws Definition

Kirchhoff’s Laws are the basic laws used in circuit analysis to solve complex circuit problems. Gustav Robert Kirchhoff gave us two laws Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL) which are widely used in circuit analysis. Kirchhoff’s Voltage Law (KVL) is based on the conservation of energy, whereas Kirchhoff’s Current Law (KCL) is based on the conservation of charge. These laws help us to calculate the resistance or impedance connected to the circuit and the current flowing through them.

Different Names of Kirchhoff’s Laws

  • Kichhoff’s Current Law is often called Kirchhoff’s First Law or Kirchhoff’s Junction Rule
  • Kirchhoff’s Voltage Law is often called Kirchhoff’s Second Law or Kirchhoff’s Loop Rule

Kirchhoff’s Current Law  or Kirchhoff’s First Law

Kirchhoff’s Current Law states that

“The total current or charge entering a junction or node is precisely equal to the total current or charge exiting the node, as no charge is lost at the node”. 

To put it another way, the algebraic sum of all currents entering and exiting a node must be zero. Kirchhoff’s Current Law (KCL) is also known as Kirchhoff’s First Law or Kirchhoff’s Junction Rule.

Note: 

Kirchhoff’s First law is similar to the Law of Conservation of charge. As a result, a Nord or junction is a point in a circuit that does not serve as a charge source or sink.

Therefore,

n∑k=1 IK = 0

Where n denotes the total number of branches at the node with currents flowing toward or away from it.

i.e. 

I(exiting)+I(entering) = 0

For Example,

In the figure shown below the node or the junction has five branches. The three incoming currents, i3, i4, and i5, and the two incoming currents, i1 and i2. Hence, According to Kirchhoff’s Current Law, the sum of total incoming and outgoing currents at the node will now equal zero. Consider the current entering the node as positive and the current exiting the node as negative then the algebraic sum can be represented as

(-I1) + (-I2) + (I3) + (I4) + (I5) = 0

⇒ I3 + I4 + I5 = I1 + I2

 

Kirchhoff's Current Law

 

It should be kept in mind that individual currents are not necessarily the same but the sum of currents entering and exiting are the same. It should be noted that there are no set rules for assigning positive and negative signs to the current. However, to avoid confusion entering current is taken as positive, and exiting current is taken as negative. 

Kirchhoff’s Voltage Law or Kirchhoff’s Second Law

Kirchhoff’s Second Law states that

The voltage drop around a loop equals the algebraic sum total of the voltage drop across every electrical component linked in the same loop for any closed network and is equal to zero.

Note

Kirchhoff’s Second Law is similar to the Law of Conservation of energy. Because the net change in the energy of a charge after it completes a closed route must be zero.

For Example,

Consider a section of a resistor network with an internal closed loop, as seen in the diagram given below. In the closed loop, we wish to write the voltage change. The total of all voltage drops between the components (mentioned as R) linked in the loop PQRSP is zero, According to Kirchhoff’s Voltage Law.

Kirchhoff’s Voltage Law

 

So for a closed loop,

n∑k=1 Vk=0

The total number of electrical components in the loop is given by n.

i.e. 

VPQ + VQR + VRS + VSP = 0

How to Apply Kirchhoff’s Laws

When using Kirchhoff’s Current Law, the currents exiting a junction must be considered negative, while the currents entering the junction must be considered positive.

Also, while using Kirchoff’s Voltage Law, we keep the same anti-clockwise or clockwise orientation from the beginning of the loop and account for all voltage decreases as negative and increases as positive. This brings us back to the initial point when the total voltage loss is zero.

Sign Conventions for Kirchhoff’s Law

Use the following convention to assign sign in the circuit provided

  • Take Positive sign for current entering the junction and negative for current leaving the junction
  • In a loop, a rise in potential difference or EMF from lower to higher is always seen as positive i.e. moving from negative to positive terminal
  • In a loop, a reduction in potential difference or EMF from higher to lower is always seen as negative i.e. moving from positive to negative terminal.
  • If the looping direction is the same as the current flowing through the circuit, the voltage drop across the resistor is considered negative.

Uses of Kirchhoff’s Law

Kirchhoff’s Law is used for following

  • It is used to find out how much current is flowing and how much voltage is dropped in various areas of the complicated circuit.
  • It aids in determining the direction of current in various circuit loops.
  • Kirchhoff’s Laws can help you comprehend how energy moves via an electric circuit.

Limitations of Kirchhoff’s Laws

There are various limitations associated with Kirchhoff’s Laws which are:

  • Kirchhoff’s Law has one fundamental flaw: it implies that there is no changing magnetic field throughout the loop’s region, which might induce a change in magnetic flux and the creation of EMF in the circuit. This might result in a calculation mistake for high-frequency AC circuits.
  • Kirchhoff also ignored the impact of the electric field generated by other circuit components.
  • Kirchhoff’s Current Law works with the premise that current only travels through conductors and wires. While parasitic capacitance can no longer be overlooked in High-Frequency circuits. Because conductors or wires are serving as transmission lines in certain circumstances, electricity may start flowing in an open circuit.

Kirchhoff’s Law Solved Examples

Example 1: Find the value of I from the circuit in the figure below.

Example 1

 

Solution:

Apply Kirchhoff’s First Law to the point P in the supplied circuit.

Consider the sign convention: positive arrows point toward P, whereas negative arrows point away from P.

As a result, we now have the following:

0.2 A – 0.4 A + 0.6 A – 0.5 A + 0.7 A – I = 0

1.5 A – 0.9 A – I = 0 

0.6 A – I = 0

I = 0.6A

Example 2: Find the value of the current passing through the resistance R1 = 10 Ω in the circuit below using Kirchhoff’s principles, when R2 and R3 both are equal and their value is 5 Ω.

Example 2

 

Solution:

Applying Kirchhoff’s Law in the above circuit, Let’s take the current ‘i’ passing through the loop in the clockwise direction

-10 + 5(i) + 5(i) + 10(i) + 5 = 0

20i -5 = 0

20i = 5

i = 5 / 20 =1/4

The current passing through R1 is 1/4 Ampere.

Also, Check

FAQs on Kirchhoff’s Law

Q1: Who gave Kirchhoff’s Laws?

Answer:

Kirchhoff’s law was discovered by a German Physicist, Gustav Robert Kirchhoff

Q2: What is Kirchhoff’s Voltage Law?

Answer:

Kirchhoff’s Second Law also called Kirchhoff’s Voltage Law states that ” For any closed network Voltage around a loop is equal to the sum of voltage drop in the same loop  and it is equal to zero.”

Q3: What is Kirchhoff’s Current Law?

Answer:

Kirchhoff’s First Law also called Kirchhoff’s Current Law states that ” Total current entering in a junction is equal to the total current leaving that junction.”

Q4: Kirchhoff’s Second Law is also known as?

Answer:

Kirchhoff’s second law is also known as  Kirchhoff’s Voltage Law.

Q5: How many Kirchhoff Laws are there?

Answer:

There are two Kirchhoff laws

  • Kirchhoff’s First Law or Kirchhoff’s Current Law
  • Kirchhoff’s Second Law or Kirchhoff’s Voltage Law

Q6: Why does Kirchhoff’s Law Fail at High Frequency?

Answer:

Because the rules KCL and KVL are incompatible with high-frequency AC circuits, Kirchhoff’s laws fail at high frequencies. At higher frequencies, the interference of induced EMF caused by changing magnetic fields becomes more severe.



Last Updated : 15 Jun, 2023
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