Kirchhoff’s Voltage Law (KVL)

Dr. Dattaraj Vidyasagar
August 25, 1996
January 1, 2024

This entry is part 9 of 12 in the series Basics of Electricity

Basics of Electricity

The KVL is the best tool to analyse the electrical and even electronic circuits. If you learn KVL properly, you will be able to read all the branches in a circuit like we read a book with all pages in it…! So don’t ignore this topic and the topic of KCL also. It is one of the most important topic in fundamentals of electricity and electronics.

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Definition

In Kirchhoff’s Voltage Law, the algebraic addition of all voltage drops in a closed circuit is always equal to zero.

To understand the law consider the following circuit. Here a battery is connected to number of resistors like R1 = 1Ω, R2 = 2Ω, R3 = 3Ω and R4 = 6Ω with battery voltage V = 12V.

The Maths

Now if we apply Ohm’s Law, we can calculate the total current in the circuit, as follows:

Total resistance of the circuit is: 12Ω. This is because all resistors are in series.

So current flowing through the circuit is: I = V/R
Voltage drop across R₁ is: V₁ = 1A x 1Ω = 1V
Voltage drop across R₂ is: V₂ = 1A x 2Ω = 2V
Voltage drop across R₃ is: V₃ = 1A x 3Ω = 3V
Voltage drop across R₄ is: V₄ = 1A x 6Ω = 6V
So we can write the equation: V = V₁ + V₂ + V₃ + V₄ = 1V + 2V + 3V + 6V = 12V

That is the algebraic addition of all voltages in the circuit, including the battery voltage (V) will be equal to zero.

V₁ + V₂ + V₃ + V₄ + (–V) = 1V + 2V + 3V + (–6V) = 0

So the general equation of Kirchhoff’s Voltage Law is given by:

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Dr. Dattaraj Vidyasagar

M.S. Electronics & Telecomm. (Cleveland Institute of Electronics, Ohio), Associate Member (IETE, Kolkata), Panelist on Dr. Homi Bhabha Foundation, Google certified educator (Level-1), Mentor of Change (MoC-1619) Niti Ayog, Government of India, International Robotics Trainer, Veteran of Applied Electronics since 35+ years.