Kirchhoff’s laws and their applications.

Introduction

To have a proper understanding of an electric circuit, it is essential to learn about the laws of electricity. One of the most important laws for solving electric circuits is Kirchhoff’s Law. With the help of Kirchhoff’s law, it becomes very easy to solve the circuits quickly and easily. Accordingly, Kirchhoff has given two laws, Kirchhoff’s current law and Kirchhoff’s voltage law. Kirchhoff’s laws help to analyze the circuit. 

Now, the question arises who Kirchhoff was? Gustav Robert Kirchhoff was a German physicist born on 12 March 1824, Konigsberg, Prussia. Initially, he started his research on the conduction of electricity. This research led him to formulate the two laws of Closed Electric Circuits in 1845, i.e. Kirchhoff’s current law and Kirchhoff’s voltage law.

What Is Kirchhoff’s law?

In 1845, Gustav Robert Kirchhoff, a German physicist, gave laws explaining the conservation of energy and current in an electric circuit. These laws help analyze and calculate the electrical impedance and resistance of a complex AC circuit. Let us now understand this concept in detail. There are two Kirchhoff’s laws:

Kirchhoff’s current law is Kirchhoff’s first law or Kirchhoff’s Junction rule. According to the Junction Rule, in an electric circuit, the total current in a junction is equal to the sum of currents outside the junction.

Kirchhoff’s Voltage law is also known as Kirchhoff’s Second law or Kirchhoff’s loop rule. According to the Loop rule, the sum of voltages around a closed electric circuit is zero. 

Kirchhoff’s current law  

Kirchhoff’s current law states, ‘The current flowing into a node or a junction must be equal to the current flowing out of it.’ 

In other words, It states that the algebraic sum of all currents in the given electric circuit is equal to zero.

Thus, this law indicates the conservation of charge. In physics, the charge is a conserved quantity, i.e. the amount of charge entering is equal to the amount of charge coming out of it.

Now, understanding this concept with some examples:

Consider a circuit in which at Node O, currents I1, I2, I3 are incoming currents, and currents I4, I5 are outgoing currents. Now, according to the Junction rule, the sum of incoming currents is equal to the outgoing currents; therefore, 

                                I1+I2+I3 = I4+I5

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

 Suppose at Node A, there are four incoming currents I1, I2 , I3, I4 and three outgoing currents I5, I6, I7.

I1= 5, I2= 10, I3= 4, I4= 7, I5=6, I6 = 12, I7 = ? Calculate I7.

According to Kirchhoff’s current law,

  I1 + I2 + I3 + I4 = I5 + I6 + I7

 I1 + I2 + I3 + I4 – I5 – I6 – I7 = 0

   5 + 10 + 4 + 7 – 6 – 12 = I7

I7 = 8

From the above examples, it is very clear that sign convention is an essential part of solving the electric circuit. Here, we consider the incoming current positive and the outgoing current as negative.

Example 1: Determine the electric current that flows in a circuit in which there are 2 batteries of 12 volts  and 3 resistors of 1,2 and 6 omegas

Solution :  

In this, the direction of current will be the same as the direction of clockwise rotation.

– I – 6I + 12 – 2I + 12 = 0

-9I + 24 = 0

-9I = -24

I = 24 / 9

I = 8 / 3 A

Kirchhoff’s voltage law

Kirchhoff’s voltage law states that in any complete loop within an electric circuit, the sum of all voltages across components that provide electrical energy must be equal to the sum of all voltages across the other elements in the same loop.

In other words, the algebraic sum of all voltages in a loop is equal to 0.

To get the proper result, it is essential to maintain the direction, either clockwise or anticlockwise.

This law indicates the law of conservation of energy.

The work is done by the electrical charges or on the electrical charges due to the electrical forces inside the electrical component.

The total work done by the charge carriers on the rest component is equal to the total work done on the charge carriers due to electrical forces. Thus, it means that the potential differences across the element are to be 0.

Procedure to solve the problem:

The algebraic sum of voltages near a closed loop should be zero.

Draw the current direction and label the voltage direction. Remember that voltage on a voltage source is always positive to the negative end.

Define either clockwise or anticlockwise direction as voltage drop direction. Once the direction is defined, the same convention is used in every loop—the sign + for the voltage in the current direction and – otherwise.

Apply KVL.

KIRCHHOFF’S Laws’ Applications

This law analyzes how the current and voltage sources work in the electric circuit.

Applications in daily life:

• In the deserts, days are very hot as sand is rough; therefore, it is a good heat absorber. Now by Kirchhoff’s Laws, a Good absorber is a good emitter. So accordingly, the nights will be cool. That’s why in deserts, days are hot and nights are cold.
• This law is used to calculate the unknown values of current and voltages in the circuit.
• Kirchhoff’s law was the first law that helped the analysis and calculation of complex circuits become manageable and easy.
• The Wheatstone bridge is an essential application of Kirchhoff’s laws. It is also used in mesh and node analysis.

Conclusion

Thus, Kirchhoff’s law is a fundamental electrical law that helps solve and analyze the electric circuit quickly. Calculating the unknown current and voltage in an electric circuit becomes easier. Kirchhoff’s first law is based on the conservation of charges, and Kirchhoff’s second law is based on energy conservation. Gustav Robert Kirchhoff described it in 1845.

Kirchhoff’s first law is junction rule or current law, and Kirchhoff’s second law is loop rule or voltage law. It is the significant and fundamental law of electricity.