# Current Dividers:

## Introduction

In this project, we will design a resistive network to draw a relatively large amount of power from a source. We will initially restrict our choice of resistors to the ceramic resistors in the Digilent® Analog Parts kit—we will see that this restriction eliminates the possibility of using a single resistor in our design. We will then design a network of parallel resistors in order to meet the power requirements.

Our design requirement is to draw a minimum of 2.5W from a source. Since the power available from the Analog Discovery™ is significantly below this level, we will use a 6V lantern battery as our voltage supply.

This exercise uses concepts introduced in our project on Current Dividers. A link to this project is provided at the right.

#### Supplemental Equipment Requirements

• This exercise will require a 6V lantern battery, in addition to the usual equipment (Analog Discovery, digital multimeter, Digilent Analog Parts Kit).

• Caution! Components may become very hot! It is our intention during this experiment to cause failure of a resistor. During this process, the resistor will become hot and may emit smoke. Do not touch the resistor during this experiment. Conduct the experiment in a well-ventilated area.

## Step 1: Determine the Desired Equivalent Resistance for the Circuit

We want to design a circuit like that shown in Fig. 1, consisting of an equivalent resistance, which will dissipate at least 2.5W from a 6V source.

From the definition of power, we need:  $2.5W \le {V_{out}} \cdot I$

## Step 2: Use a Single Resistor to Meet Requirements

Choose a single carbon resistor (one of the small resistors with color bands from your parts kit) which meets the requirement determined in Step 1. Calculate the expected power which will be absorbed by the resistor. Set up your circuit to measure I and Vout. Connect the resistor to the 6V battery; record I and Vout.

Note: it is inevitable that the resistor will burn out and start to smoke. This is a good indication that the resistor's power limitations have been exceeded. Disconnect the power supply from the resistor when this happens.

## Step 3: Use a Set of Parallel 47Ω Resistors to Meet the Requirement

Create a set of 47Ω resistors in parallel, as shown in Fig. 2, which provide an equivalent resistance that meets the requirement determined in Step 1. Set up your circuit to measure I and Vout. Connect the resistor to the 6V battery; record I and Vout.

## Step 4: Compare Resistor Power Absorption for Both Cases

From your measured currents and resistor voltages, calculate the power dissipation per resistor for Steps 2 and 3 above. Compare the power dissipated by the 47Ω resistors with the power dissipated when using the resistor of Step 2.

## Step 5: Compare Resistor Power Absorption for Both Cases

1. Try using 68Ω resistors in a parallel configuration to meet the design requirements. What is the expected power dissipation per resistor for your design?

2. With the resistors in the Digilent Analog Parts kit, can you use a series combination of resistors to meet the design requirement without burning out the resistors?

3. Try using the wire-wound 6.8Ω resistor to meet the design requirement. Is using that single resistor a valid design solution? What would be the drawback of using the larger resistor in a mass-produced design? (Hint: How much do you think the wire wound resistor costs, compared to the carbon resistors?)