The time was 1845, and it was the era of research and experiments when the German physicist Gustav Kirchhoff laid down two basic principles that became vital in electrical engineering and circuit analysis. These two laws mainly deal with the conservation of energy and conservation of current through the circuit and help in analysing complex electrical circuits and calculating the electrical resistance of such networks.

These two laws are as follows.

1. Kirchhoff’s current law is derived from the principle of conservation of charge and is also known as Kirchhoff’s junction rule or the first law.
2. Kirchhoff’s voltage law is based on the principle of conservation of energy and is also called Kirchhoff’s loop law or the second law.

Kirchhoff’s current law

This law is also known as Kirchhoff’s first law or the junction law. The arithmetic sum of all the currents directed towards a point in a circuit is equal in magnitude to the algebraic summation of all the currents directed away from the point.

In other words, at any junction, the sum of currents entering the junction is equal to the sum of currents leaving the junction.

• This circuit law is based on the principle of conservation of charge because when the current is steady, there is no accumulation/deposition of charges (Q) at any junction or even at any point in the wire.
• Thus, the total current flowing in must be equal to the total current flowing out.
• I (entering) = I(exit) or, I(enter) – I(exit) = 0

Calculation

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

Kirchhoff’s Voltage Law

This is also known as the loop law or Kirchhoff’s second law. The arithmetic sum of all the potential differences along a closed loop in the electric circuit totals zero.

That is, the algebraic sum of changes in potential around any closed loop involving resistor elements and the cells in the closed-loop is zero.

This law is based on the principle of the law of conservation of energy.

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.

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

Kirchhoff’s voltage and current laws establish a connection between the circuit elements. These laws can help us better understand complex circuit networks and resolve them.

Some conventions:

Potential across a resistor is negative in the direction of the current, whereas potential across a resistor is positive in the direction opposite to the current.

Potential is gained on crossing the battery from the negative to the positive terminal, whereas potential drops on crossing the battery from the positive to the negative terminal.