# Kirchhoff's Current Law:

## Introduction

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

Kirchhoff's current law (KCL) tells us that the sum of the currents entering (or leaving) a node is zero. More background material 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 current law by measuring currents at a node.
• 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. Verify KCL

1. Write KCL at node A, as indicated on the schematic to the right. Use the given reference current directions. Your equation should look like this:

• Node A: - I1 + I2 - I3 = 0
2. Use your DMM as an ammeter to measure the currents I1 , I2 , and I3 shown on the schematic. Make your measurements to be consistent with the given reference directions.

3. Substitute your measured currents from part 2 into the KCL equation you determined in part 1. Verify that KCL is satisfied.

#### C. Check the Passive Sign Convention

1. Verify that the passive sign convention is obeyed for the currents in 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 KCL is still obeyed.

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

3. Change the reference direction of the current I1 in part B. Re-write KCL at node A to reflect this change. Re-measure the current I1 and verify that KCL is still obeyed.

4. Incorporate a fourth resistor, R4 , as shown in the circuit below. Write KCL around Node B using the given reference current directions. Verify that KCL is satisfied.

#### Challenge Problems

• If you are confident with your knowledge on Kirchhoff's current 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.