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Parallel Resistances

Project 5: Resistors

tag Analog Discovery Resistance Parallel

Resistors:

Parallel Resistances

Introduction

Related Material:
Parallel Elements

When resistors are connected in parallel, the combination has an equivalent conductance that is the sum of the conductances of the individual resistors. In terms of resistance, for a set of N series resistors, this can be stated mathematically as:

\[{R_{eq}} = \frac{1}{{\frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \cdots \frac{1}{{{R_N}}}}}\]

Where R1, R2, ..., RN are the resistances of the N individual resistors.

This property can be useful in creating desired resistance values from a limited selection of fixed resistors. In this project, we will create a 5 kΩ resistor from the resistors available in Digilent's analog parts kit.

Before you begin, you should:
  • Be able to use V+ to apply power to a circuit on your breadboard.
  • Know how to measure current using a DMM or other instruments.
  • Be able to construct a physical circuit from its schematic.

Inventory:

Qty Description Typical Image Schematic Symbol Breadboard Image
2 10 kΩ Resistor
1 Digital Multimeter (DMM)

Procedures

Step 1: Construct the Circuit

  1. Connect the resistors in parallel and use V+ to apply 5V voltage across the resistors, as shown.

  2. You will use your DMM to measure the current I into the series combination of resistors.

Step 2: Verify Overall Equivalent Resistance

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

  2. Measure the current I.

  3. Using the current I, the 5V across the series combination of resistors, and Ohm's law, calculate the equivalent resistance of the series resistors, Req.

  4. Using the equivalent resistance formula from the introduction and the measured resistances of the individual resistors, calculate the expected resistance of the series combination of resistors.

  5. Calculate the percent error between the expected value and the measured value of the equivalent resistance. Use the formula below to do this.

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

Test Your Knowledge!

  1. Use your DMM to measure the resistance of the combination of parallel resistors. (Be sure to disconnect the voltage source from the resistors before you do this—you DO NOT want to include the resistance of the voltage source in your measurement.)

    Calculate a percent error between the resistance measured with your DMM and the expected resistance you determined in Part 4 of Step 2. Use the formula provided in Step 2.

  2. Add resistors to the circuit in this project to create a 3.3 kΩ resistor. Measure the resistance of the circuit you created and compare your expected value with the measured value. How close can you get to the design requirement?

  • Other product and company names mentioned herein are trademarks or trade names of their respective companies. © 2014 Digilent Inc. All rights reserved.
  • Circuit and breadboard images were created using Fritzing.