Kirchhoff's Voltage Law: Statement, Formula, Diagram and Solved Examples

Kirchhoff's voltage law is one of the most important rules used to analyze electrical circuits. It explains how voltage is distributed in a closed loop and shows that the total voltage supplied by a source is equal to the total voltage used by the components in the circuit.

Have you ever wondered why a battery, wire, and bulb work together smoothly in a circuit? The answer lies in the way electrical energy is transferred and used within a closed loop. Knowing what Kirchhoff's voltage law is helps students understand how electrical circuits follow the principle of energy conservation.

This is a perfect guide to state Kirchhoff's voltage law, its statement, formula, diagram, applications, advantages, limitations, and solved examples in a simple way.

Table of Contents

• What is Kirchhoff's Voltage Law
• How to Apply Kirchhoff's Voltage Law
• Solved Example of Kirchhoff's Voltage Law
• Advantages and Disadvantages of Kirchhoff's Voltage Law
• Frequently Asked Questions on Kirchhoff's Voltage Law

What is Kirchhoff's Voltage Law

Kirchhoff's Voltage Law (KVL), which is also known as the loop rule, states that the total voltage in any closed electrical loop is equal to zero. In simple words, the total voltage supplied by the source is equal to the total voltage used by the components in that loop.

The fact is that electrical energy is conserved in a circuit. Whatever energy is provided by the battery must be used by the resistors, bulbs, or other devices connected in the circuit.

Interestingly! This law was introduced by German physicist Gustav Kirchhoff and is widely used in electrical and electronics engineering.

"Kirchhoff's voltage law states that the algebraic sum of all voltages around any closed loop in an electrical circuit is equal to zero.”

Mathematically, it can be represented as, 

∑V=0

This means, 

Total Voltage Rise = Total Voltage Drop

Now, let's first try to understand the mathematical form of the law.

For a closed loop:

$V_{AB}+V_{BC}+V_{CD}+V_{AD}+...+V_n=0$

 

Where, 

•  $V_{AB}, V_{BC}, V_{CD}, V_{AD}$ are voltages in the loop
• Positive values represent voltage rises
• Negative values represent voltage drops

How to Apply Kirchhoff's Voltage Law

Kirchhoff's second law is applied by selecting a closed loop and adding all the voltage rises and voltage drops along that loop. According to the law, the total voltage around the loop must be zero.

The circuit contains two closed loops, namely Loop 1 and Loop 2. We can apply Kirchhoff's voltage law to either loop separately.

Step 1: Select a Closed Loop

Choose one closed path in the circuit. For example, start with Loop 1.

Step 2: Choose a Direction

Move around the loop in a single direction, either clockwise or counterclockwise. The direction should remain the same throughout the calculation.

Step 3: Identify Voltage Rises and Voltage Drops

As you move around the loop:

• Crossing a battery from the negative terminal to the positive terminal gives a voltage rise (+).
• Passing through a resistor in the direction of current flow gives a voltage drop (-).

Step 4: Add All Voltages

Add all the voltage rises and voltage drops in the loop using their signs.

Step 5: Apply Kirchhoff's Voltage Law

According to Kirchhoff's second law:

∑V=0

This means that the total voltage supplied by the battery is equal to the total voltage lost across the resistors.

Imagine starting at point A and moving around Loop 1 until you return to the same point. Along the way, the voltage may increase when passing through the battery and decrease when passing through the resistor.

When you finally return to point A, the total change in voltage becomes zero because you are back at the same electrical potential. The same principle applies to Loop 2.

In simple words, the energy gained by a charge from the battery is equal to the energy lost while moving through the circuit components. This is why Kirchhoff's second law follows the principle of conservation of energy.

Solved Example of Kirchhoff's Voltage Law

Consider the circuit shown in the diagram above.

 It contains,

• A voltage source of 24 V
• Three resistors connected in series:
•  $R_1$=12Ω
•  $R_2$=24Ω
•  $R_3$=12Ω

Step 1: Calculate the Total Resistance

Since the resistors are connected in series:

$R_{total}=R_1+R_2+R_3$

$R_{total}=12+24+12$

$R_{total}=48Ω$

Step 2: Find the Current in the Circuit

Using Ohm's Law:

$I=\frac{V}{R}$

$I=\frac{24}{48}$

I=0.5A

Thus, the current flowing through the circuit is 0.5 A.

Step 3: Calculate the Voltage Drop Across Each Resistor

Using:

V=IR

For  $R_1$

$V_{R_1}=0.5\times12$

$V_{R_1}=6V$

For  $R_2$

$V_{R_2}=0.5\times24$

$V_{R_2}=12V$

For  $R_3$,

$V_{R_3}=0.5\times12$

$V_{R_3}=6V$

Step 4: Verify Kirchhoff's Voltage Law

Moving clockwise around the loop:

• Voltage rise from the source = 24 V
• Total voltage drops = 6 V + 12 V + 6 V

Applying Kirchhoff's Voltage Law:

$V_s-V_{R_1}-V_{R_2}-V_{R_3}=0$

 24−6−12−6=0

24−24=0

0=0 

The total voltage supplied by the battery is equal to the total voltage drop across the resistors.

24V=6V+12V+6V

This confirms that Kirchhoff's voltage law is satisfied and shows that electrical energy is conserved within the closed loop.

Advantages and Disadvantages of Kirchhoff's Voltage Law

Kirchhoff's voltage law is widely used for studying electrical circuits because it helps explain how voltage behaves in a closed loop. Like any scientific principle, it has both advantages and limitations.

Advantages of Kirchhoff's Voltage Law

• Helps Calculate Unknown Voltages: Kirchhoff's Voltage Law makes it easier to determine unknown voltage values in a circuit by relating voltage rises and voltage drops.
• Simplifies Circuit Analysis: It provides a systematic way to analyse electrical circuits, making complex circuit problems easier to solve.
• Useful for Closed-Loop Circuits: The law can be applied to simple as well as complex closed-loop circuits to find missing electrical quantities.
• Based on Conservation of Energy: Kirchhoff's voltage law follows the principle of conservation of energy, which makes it a reliable tool for circuit calculations.

Disadvantages of Kirchhoff's Voltage Law

• Not Suitable for Rapidly Changing Magnetic Fields: The law assumes that no changing magnetic field is present within the loop. If the magnetic field changes rapidly, additional voltages may be induced, affecting the accuracy of the results.
• Limited in Certain Advanced Circuits: In some high-frequency or electromagnetic systems, Kirchhoff's voltage law alone may not be sufficient, and more advanced methods may be required.

In this article, we learnt that Kirchhoff's voltage law states that the algebraic sum of all voltages in a closed loop is equal to zero. We also studied its formula, diagram, applications, advantages, limitations, and a solved example. This law plays an important role in circuit analysis by showing that the total voltage rise in a loop is always equal to the total voltage drop.