 # Kirchhoff's Voltage Law:

## Introduction

In this project, we will make measurements to verify that Kirchhoff's voltage law is satisfied for some relatively arbitrary circuit.

Kirchhoff's voltage law (KVL) tells us that the sum of the voltage differences around any closed loop in a circuit is zero. More detail relative to Kirchhoff's important laws are provided in the links to the right.

We will also use this project to gain some experience with the passive sign convention. The passive sign convention tells us that, for passive circuit elements, we must assume a consistent voltage polarity and current direction: positive current must be assumed to enter the positive voltage terminal. Although the passive sign convention won't become terribly important to us until we start applying voltage-current relations for circuit elements, we should start using it now in order to avoid confusion later.

##### Before you begin, you should:
• Complete the first Circuit Implementation project.
• Be able to determine a resistor's resistance from its color code. More information regarding resistor color codes can be found in the related materials section above.
##### After you're done, you should:
• Verify Kirchhoff's voltage law by measuring voltage around a closed loop in a circuit.
• Choose circuit variables (voltages and currents) according to the passive sign convention.
• Be able to complete the Challenge problems at the end of this exercise.

## Inventory:

Qty Description Typical Image Schematic Symbol Breadboard Image
3 Resistors with red as the third color band

(They will be in the 1kΩ to 9.9kΩ range)   ## Step 1: Understanding the Circuit

#### A. Circuit Schematic

1. Use V+ to implement the voltage source.

2. Connect resistors as shown.

#### B. Write out your KVL equations

1. Write KVL around loops 1 and 2, as indicated on the schematic to the right. Use the given reference voltage polarities. Your equations should look something like this:

• Loop 1: -5V - V1 - V3 = 0
• Loop 2: -5V - V1 + V2 = 0

#### C. Verify KVL

1. Use a voltmeter to measure the voltages V1 , V2 , and V3 shown on the schematic. Make your measurements to be consistent with the given reference directions.

2. Substitute your measured voltages from part 1 into the KVL equations you determined in section B. Verify that KVL is satisfied for both of the loops.

#### D. Check the passive sign convention

1. Verify that the passive sign convention is obeyed relative to the voltages of part B.

1. Exchange any of the resistors for a resistor with a different value (as long as it has a red third color band) and verify that KVL is still obeyed.

2. Change the 5V voltage source for a -3V source. (You will have to use the AWG to apply the voltage.) Verify that KVL still works.

3. Change the reference polarity of the voltage V1 in part B. Re-write KVL around loop 1 to reflect this change. Re-measure the voltage V1 and verify that KVL is still obeyed.

4. We've added a third loop in the circuit below. Write KVL around loop 3 using the given reference polarity and verify that KVL is satisfied.

#### Challenge Problems

• If you are confident with your knowledge on Kirchhoff's voltage law and would like some extra practice, we have provided some extra problems in the links below. These problems require that you understand the concepts introduced throughout this exercise.