What is Kirchhoff's Voltage Law (KVL)?
1 Answer
Understanding Kirchhoff's Voltage Law (KVL): A Simple Guide
Kirchhoff's Voltage Law, commonly abbreviated as KVL, is a fundamental principle in electrical engineering and a cornerstone of circuit analysis. Alongside Kirchhoff's Current Law (KCL), it provides a powerful method for understanding and calculating the behavior of electrical circuits.
This guide will break down the definition of KVL, its mathematical formulas, and a practical example to help you master this essential concept.
What is Kirchhoff's Voltage Law (KVL)?
Kirchhoff's Voltage Law is based on the principle of conservation of energy. It states that for any path an electrical charge takes around a closed loop, its net change in energy must be zero. In terms of voltage, this is expressed as:
The algebraic sum of all voltages around any closed loop in a circuit is equal to zero.
A closed loop (or mesh) is simply any continuous path in a circuit that starts and ends at the same point. As you trace this path, you will encounter components that either supply energy (voltage rises) or consume energy (voltage drops). KVL states that the total energy supplied must equal the total energy consumed within that loop.
The KVL Formulas
Kirchhoff's Voltage Law can be expressed mathematically in two common and equivalent ways.
1. The Algebraic Sum Method
This is the most formal definition of KVL. It states that if you sum all the voltage rises and drops around a loop—assigning a positive sign to rises and a negative sign to drops (or vice versa, as long as you are consistent)—the total will be zero.
The formula is:
Σ Vₖ = 0
Where:
Σ is the summation symbol.
Vₖ is the voltage across the kth element in the loop.
* The sum is taken for all elements around a closed loop.
2. The Voltage Rises vs. Voltage Drops Method
This is often a more intuitive way to apply KVL. It separates the voltage sources (rises) from the voltage consumers (drops).
The formula is:
Σ v_rise = Σ v_drop
This simply means:
> Sum of voltage rises = Sum of voltage drops
- A voltage rise occurs when moving through a component from the negative (-) to the positive (+) terminal, such as a battery or power supply.
- A voltage drop occurs when moving through a component from the positive (+) to the negative (-) terminal, typically across a resistor as it dissipates energy.
KVL Example Explained
Let's apply KVL to the simple series circuit shown in the diagram.
Image shows a circuit with a voltage source Vₛ and three resistors R₁, R₂, and R₃ in series. The voltage drops across the resistors are V₁, V₂, and V₃ respectively.
The circuit consists of:
A voltage source Vₛ
Three resistors R₁, R₂, and R₃
* The voltage drops across these resistors are V₁, V₂, and V₃.
A red arrow indicates a clockwise path for our analysis. Let's apply both KVL methods.
Method 1: Algebraic Sum (Σ Vₖ = 0)
We'll start at the bottom of the voltage source and move clockwise around the loop:
- Vₛ: We move from the negative (-) terminal to the positive (+) terminal. This is a voltage rise, so we'll give it a positive sign: +Vₛ.
- V₁: We move through resistor R₁ from its positive (+) side to its negative (-) side. This is a voltage drop: -V₁.
- V₂: We move through resistor R₂ from its positive (+) side to its negative (-) side. This is another voltage drop: -V₂.
- V₃: We move through resistor R₃ from its positive (+) side to its negative (-) side. This is a final voltage drop: -V₃.
Summing these up according to the formula, we get:
Vₛ - V₁ - V₂ - V₃ = 0
Method 2: Rises vs. Drops (Σ v_rise = Σ v_drop)
- Identify Voltage Rises: In this loop, the only element providing a voltage rise is the source, Vₛ.
- Identify Voltage Drops: The resistors R₁, R₂, and R₃ cause voltage drops of V₁, V₂, and V₃.
Equating the sum of rises to the sum of drops gives us:
Vₛ = V₁ + V₂ + V₃
As you can see, both equations are algebraically identical and represent the same physical principle. This confirms that in a series circuit, the source voltage is divided among the components in the loop.
Summary
- Kirchhoff's Voltage Law (KVL) states the algebraic sum of voltages around any closed loop is zero.
- It is a consequence of the law of conservation of energy.
- It can be expressed as Σ Vₖ = 0 or Σ v_rise = Σ v_drop.
- KVL is a critical tool for analyzing any electrical circuit, from the simplest series circuit to complex networks.