Electrical Circuit Analysis

Introduction

Kirchhoff’s Voltage Law is a common and simple way to analyze a circuit. This one requires a little math so put your math hat on! Also, if you have not reviewed my other posts in DC circuits, please do so.

DC Circuits – Basics
DC Circuits – Series vs Parallel

Kirchhoff’s Voltage Law

Kirchhoff’s Voltage Law (KVL) is a method for analyzing DC circuits. It states that in any loop of the circuit, the net voltage must be zero. That means that if you add up all the components that are adding voltage and subtract all the components that are using voltage, they should equal zero.

When determining if a component adds or subtracts voltage, you need to look at the signs. Pick a starting point for your loop that is not a component. As you travel around the loop, if you find a component that is labeled with a negative symbol followed by a positive symbol, you are adding voltage to the circuit. If the component has a positive symbol followed by a negative symbol, you are subtracting voltage from the circuit.

Sometimes resistors will not have a voltage label. They instead have their value in Ohms. To find their voltage, we need to multiply the value of the resistor by the current (I), per Ohm’s Law. If the current is not known, then you will have some extra steps. The example below will cover this.

Example 1.

In this example, we have two loops. Loop one has two power sources and two resistors. Loop 2 has a power source and two resistors. We will analyze this circuit using Kirchhoff’s Voltage Law. Both loops are treated at independent circuits using KVL.

Steps to Solve Using KVL

Step 1: Label the loop and the components as in Figure DC-3-1. The direction of the loop is not important, but most people choose clockwise.
Step 2: Pick a starting point. I usually pick the bottom left corner of the loop as my starting point, but you can pick any point you like.
Step 3: Add up the voltages in the circuit. If you don’t know the voltage, use Ohm’s Law to give the equivalent in terms of what you do have.

Loop 1

Add the voltages of the components:

Notice how we label the voltages of the resistors as the value of the resistor times the current. That is because V = IR or voltage is equal to current times resistance. For the most part, we label resistors as voltage drops. Now that we have the components listed, we can simplify by adding like terms.

Next, we will move the term with the current over to the other side and then solve for current.

Now that we know the current for loop 1, we can go back and find the voltage drop across the resistors R1 and R2.

Loop 2

We can use the same procedure to analyze loop 2.

Quick Check

Do our answers make sense? The total resistance of loop 1 is 12Ω, and if the total voltage is 12V, then the current should be 1A. The total resistance of loop 2 is 8Ω. We know from analyzing parallel circuits that if the resistance of one loop is lower than the resistance of another, more current will flow through the loop with the least amount of resistance. Loop 2 having a higher current flow, checks out.

Signs

Signs on the voltage sources are important. You need to know which side has the higher potential (higher voltage), so you can correctly account for the voltage in the system. The signs on the resistors and even the direction the current flows is less important. If you happen to get a negative number on the current, that means that the current is flowing the other direction.

Thank You

Thank you for taking the time to read this post. I hope that you learned something or at least got a refresher. Feel free to leave questions or comments below. If you like this content and want to see more, please consider subscribing. It really helps me provide more content for you. Or, if you feel we are worthy, consider leaving a tip.