Understanding Kirchhoff’s Voltage Rule

Gustav Robert Kirchhoff, a German scientist, was born in Konigsberg, Prussia, on March 12, 1824. His first study area was electricity conduction. Kirchhoff developed the Laws of Closed Electric Circuits in 1845 due to his study. Kirchhoff’s Voltage and Current Laws are the names given to these laws after he was identified. Because these regulations apply to all circuits, grasping their foundations is critical to comprehending how an electronic circuit works. Although Kirchhoff’s rules have made him famous in the engineering industry, he has made further discoveries. He was the first to demonstrate that an electrical activity could move at the velocity of light.

These principles aid in determining the resistance of a complex system or impedance in the case of alternating current and the current flow in the network’s many streams. Let’s look at what these laws say in the following part.

Kirchhoff’s Rule

Kirchhoff’s Current Law is also known as Kirchhoff’s First Law and Kirchhoff’s Junction Rule. The Junction rule states that the sum of currents in a junction equals the sum of currents outside the intersection in a circuit.

Kirchhoff’s Voltage Law is also known as Kirchhoff’s Second Law or Kirchhoff’s Loop Rule. According to Kirchhoff’s loop rule, the sum of the voltages around the closed loop is equal to zero.

Kirchhoff’s Voltage Law

Kirchhoff’s Voltage Law states that “For every closed network, the voltage surrounding a loop equals the total of all voltage drops in the same loop, and it also equals zero.”

In other words, the algebraic total of all voltages in the loop must equal zero, and this characteristic of Kirchhoff’s rule is known as energy conservation.

When you start at any position in the loop and continue the same way, notice how the voltage declines in all directions, whether positive or negative and then return to the same spot. It is critical to keep the heading, whether counterclockwise or clockwise; otherwise, the final voltage value will not be zero. The voltage law may also be used to analyse series circuits.

When analysing either AC or DC circuits using Kirchhoff’s circuit rules, you must be familiar with all terminology and concepts characterising circuit components such as routers, nodes, meshes, and loops.

Sign Rules

Whenever Kirchhoff’s Voltage Law is applied to a closed-loop or a mesh algebraic total of EMFs and voltage dips are considered. As a result, EMFs and voltage dips must be appropriately labelled.

Growth in potential should be seen as positive, whereas a decrease in potential should be negative.

Steps to apply Kirchhoff’s Voltage Law

• Specify the direction of current flow in each branch of the circuit using Kirchhoff’s Current Law.
• Choose as many closed circuits as there are unknown values.
• Find the algebraic total of the voltage drops and EMFs in the circuit and set it to zero.
• If the estimated total current has a positive sign after solving the issue, the assumed direction is accurate. If it bears a negative sign, it signifies that the natural direction of current flow is the inverse of the anticipated direction.

Applications of Kirchhoff’s Laws

Kirchhoff’s rules are used to examine exceedingly complicated electrical circuits because they aid in simplifying the circuits and computing the quantum of current and voltage in circuits by making calculating unknown currents and voltages simple. The sole constraint in using these principles is that they only hold if there is no varying magnetic flux in the closed – loop system, which may not be the case.

Example of Kirchhoff’s Law 

Three resistors with resistance values of 15 ohms, 25 ohms, and 20 ohms are connected in series across a 12-volt battery supply. Calculate:

1. The total resistance.
2. The circuit currents.
3. The current through each resistor.
4. The voltage drops across each resistor.
5. Confirm the validity of Kirchhoff’s voltage law, KVL.

Total Resistance 

Since, the resistors are in series combination. So, the total resistance will be the sum of all the three resistors

R = R₁+R₂+R₃

R=15+25+20

R= 60 ohm.

The Circuit Current 

Total Current(I) = Total Voltage drop/Total Resistance

                      I = 12/60

                     I = 1/5 = 0.2 A

Current Through Each Resistor

Because the resistors are linked in series, they all seem to be part of the same loop and hence absorb the same flow of charge. So,

Current in R1 = Current in R2 = Current in R3 = Total Current = 0.2 A

1. Voltage across each Resistor

V₁ = IR₁ = 0.2×15 = 3 V

V₂ = IR₂ = 0.2×25 = 5 V

V₃ = IR₃ = 0.2×20 = 4 V

Verification 

Kirchhoff’s Voltage Law states that the summation of voltage across the circuit is zero.

Total voltage + (-V₁) + (-V₂) + (-V₃) = 12 + (-3) + (-5) + (-4)

 = 12 – 12

 = 0 = RHS

As a result, Kirchhoff’s voltage law stays true since the discrete voltage drops in around the closed-loop sum up the total voltage drop.

Conclusion

The theory behind Kirchhoff’s second law is also referred to as the law of conservation of voltage, and it is especially relevant when working with series circuits since series circuits also operate as voltage dividers. The voltage divider circuit is an essential application of many series circuits. This was all about Kirchhoff’s Voltage Law.