# Power Conservation:

## Introduction

In this project, we will illustrate how power conservation is obeyed for a simple circuit by working through the example provided in this procedure.

Power, for electrical circuit elements, is the product of the voltage across the element and the current through the element. The sign of the power indicates whether the circuit element is absorbing or generating power:

• If the voltage and current for the element agree with the passive sign convention (e.g. if the current actually does enter the positive voltage terminal) then the power is positive and power is absorbed .
• If the voltage and current do not agree with the passive sign convention (e.g. if the current enters the negative voltage terminal or if current leaves the positive voltage terminal) then the power is negative and the element is generating power.
Additional details relative to the concepts of power and passive sign convention are provided in the links to the right.

##### 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.
• Be able to determine whether a circuit element is absorbing or generating power from the element's voltage and current.
• Choose circuit variables (voltages and currents) according to the passive sign convention.
##### After you're done, you should:
• Calculate power from measured voltages and currents.
• Verify that power is conserved in an arbitrary circuit.

## 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 displayed in the image to the right.

3. Connect ground (, the black wire) as shown.

#### D. Check the Passive Sign Convention

1. Define voltages and currents for the three resistors shown in the schematic of part A. Make sure that the voltages and currents obey the passive sign convention.

## Step 2: Set Up Instruments

#### A. Create Circuit

1. Assign your resistors to R1 , R2 , R3 and set up the circuit from Step 1.

2. Open up the Voltmeter Instrument to take the necessary measurements.

3. Turn on the V+ power source by opening up the Voltage Instrument in the WaveForms™ program.

#### B. Verify that Power is Conserved

1. Measure voltage and current for all resistors in the circuit. Your voltage measurements should be consistent with the polarities you defined in Step 1.

2. Calculate the power for each of the resistors. (Hint: all of the resistors should be absorbing power.)

3. Measure the current through the 5V source. Calculate the power for the source. (Note: this power should probably be negative, since the only other elements in the circuit absorb power and something in the circuit needs to generate power.)

4. Sum the power in all the elements. Show that it is approximately zero.

• Power is the product of voltage and current, $p = i \cdot v$. Ohm's law states that the voltage across a resistor is the product of the resistor's current and its resistance, $v = i \cdot R$ . If we substitute Ohm's law into the power equation, we can solve for a resistor's power in terms only of its voltage1:
• $p = \frac{{{v^2}}}{R}$