# Resistors:

## Introduction

If the total voltage difference across a set of series resistors is known, the voltage differences across any individual resistor can be determined by the concept of voltage division. In essence, the total voltage across the series combination is divided among the individual resistors; the ratio of the voltage across each individual resistor to the total voltage is the same as the ratio of the resistor to the total resistance. These concepts are used when creating voltage dividers; linear circuits that produce an output voltage (VOUT) that is a fraction of its input voltage (VIN).

For the case of two series resistors, as shown in the figure below, the individual voltages across each resistor can be calculated according to the voltage division formulae below:

${v_1} = \frac{{{R_1}}}{{{R_1} + {R_2}}}v$ ${v_2} = \frac{{{R_2}}}{{{R_1} + {R_2}}}v$
##### Before you begin, you should:
• Understand how to measure voltage and resistance using a DMM.
• Be able to create a series circuit on a breadboard.
• Understand and know how to apply Kirchhoff's Voltage Law.

## Inventory:

Qty Description Typical Image Schematic Symbol Breadboard Image
1 1kΩ Resistor
1 2.2kΩ Resistor
1 Digital Multimeter (DMM)

## Step 1: Understanding the Circuit

1. Use your DMM to measure the resistance of both resistors. Record these resistances and use these values in Part D when making predictions.

#### A. Circuit Schematic

1. Use V+ to apply 5V voltage across the resistors.

2. Use the Analog Discovery™ voltmeter or your DMM to measure the voltage difference (VOUT) across the 2.2 kΩ resistor.

#### B. Create Circuit

1. Connect V+ (red wire) to the 1 kΩ resistor.

2. Connect the 2.2 kΩ resistor to the 1 kΩ resistor.

3. Connect 1+ (orange wire) and 1- (orange and white striped wire) across the 2.2 kΩ resistor, with 1+ on the side closest to V+.

#### C. Verify Voltage Divider Formula

1. Apply power to the circuit. (Open the voltage instrument, turn on V+.)

2. Measure the voltage VOUT.

3. Using the voltage division formula and your measured resistances from part A, calculate the expected output voltage VOUT.

4. Calculate the percent error between the expected value and the measured value of the voltage. Use the formula below to do this.

${\rm{Percent Difference = }}\frac{{{\rm{Measured Value - Expected Value}}}}{{{\rm{Expected Value}}}}x100$