Difference between revisions of "Lab 1 TF EIM"

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Kirchoff's Law
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=Kirchoff's Law (50 pnts)=
  
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Construct the circuit below.
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== Smokey Circuits==
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When doing these labs it is important to determine the limitations of your electrical components in order to avoid damaging them.
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This lab uses resistors.  Resistors are vulnerable to melting if you push too much current through them.
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Resistors have power ratings ranging from 1/8 Watt up to several Watts.  The common resistors are rated at 1/4 Watt.  Let's assume this rating for the resistors in this lab.
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Determine the maximum voltage of the DC power supply you will use. (ie, 30 Volts)
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;<math> P =I^2R = \frac{V^2}{R}< 1/4 </math> Watt
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;<math> \Rightarrow R > \frac{V^2}{1/4 Watt}=\frac{\left (30 V \right)^2}{1/4 \mbox{Watt}} = 3600 \Omega</math>
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:By keeping your resistance values above 3600 <math>\Omega</math> you should be able to avoid burning up 1/4 Watt resistors when your max voltage is 30 Volts.
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The next objective is to use resistors which allow currents that you can measure with your voltmeter.
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;Since <math>V=IR \Rightarrow I = V/R = 30 \mbox{Volts}/3600 \Omega = 8\mbox{mA}</math>
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Determine the range of currents which the voltmeter can measure. (ie 1 mA)
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To get measurable currents you need low resistance BUT the lower resistances will need to have a high power rating.  These two competing properties limit the range of resistances you can use.
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Select the three resistors you should use for this experiment.
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==Construct the circuit below==
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[[File:TF_EIM_Lab1.png | 400 px]]
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==Enter the values of the DC voltage and Resisters that you used.==
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Use a voltmeter to measure the potential difference and resistances.
  
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Enter the values of the DC voltage and all resisters
 
 
{| border="3"  cellpadding="20" cellspacing="0"
 
{| border="3"  cellpadding="20" cellspacing="0"
 
|Variable ||Measured Value
 
|Variable ||Measured Value
 
|-
 
|-
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| <math>V_{ab}</math> ||   
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| <math>V_A </math> ||   
 
|-
 
|-
 
| <math>R_1</math> ||   
 
| <math>R_1</math> ||   
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|}
 
|}
  
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Enter the measured and predicted quantities in the table below
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==Enter the measured and predicted quantities in the table below==
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Given <math>V_A</math> and the values of all resistors, use Kirchoff's laws to calculate BY HAND the
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a.) Predict the value of <math>V_B</math>
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b.) Predict the values of the three currents.
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c.) compare your predictions and measurements  by filling in the table below.
  
 
{| border="3"  cellpadding="20" cellspacing="0"
 
{| border="3"  cellpadding="20" cellspacing="0"
 
|Variable ||Measured Value|| Predicted Value|| % Difference
 
|Variable ||Measured Value|| Predicted Value|| % Difference
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|-
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| <math>V_B</math> ||  || ||
 
|-
 
|-
 
| <math>I_1</math> ||  || ||  
 
| <math>I_1</math> ||  || ||  
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|}
 
|}
  
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= Internal resistance (30 pnts)=
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Measure the internal resistance of a "D" cell battery by graphing the current on the x-axis and the measured voltage on the y-axis for several values of the resistance <math>R_L</math> shown in the circuit below.  Begin with <math>R_L = 1k\Omega</math> and then decrease it by a factor of 5 for each subsequent measurement.  You can use a volt meter to measure the current and potential difference.
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[[File:TF_EIM_Lab1a_fig.png | 200px]][[File:TF_EIM_Lab1b_fig.png | 350px]]
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{| border="3"  cellpadding="20" cellspacing="0"
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| R_{Load} (<math>\Omega</math>) || V (Volts)|| I (mA)
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|-
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| 0.5|| ||
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|-
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| 10|| ||
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|-
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| 47|| ||
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|-
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| 93|| ||
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|-
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|990 || ||
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|}
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<math>V_A - V_B = IR_{Load} = V_{bb} - I R_{int}</math>
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<math>(V_A - V_B) = - R_{int} I +  V_{bb}</math>
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<math>y = mx+b \Rightarrow R_{int} =</math> slope of V-vs- I plot
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=Questions (20 pnts)=
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#What conservation law is involved in Kirchoff's Loop Theorem?
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#What does the slope in the internal resistance plot above represent?
  
  
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Use Kirchoff's laws to predict the current values and compare them to your measurements  by filling in the table below.
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[[Forest_Electronic_Instrumentation_and_Measurement]]

Latest revision as of 17:44, 20 January 2015

Kirchoff's Law (50 pnts)

Smokey Circuits

When doing these labs it is important to determine the limitations of your electrical components in order to avoid damaging them.

This lab uses resistors. Resistors are vulnerable to melting if you push too much current through them.

Resistors have power ratings ranging from 1/8 Watt up to several Watts. The common resistors are rated at 1/4 Watt. Let's assume this rating for the resistors in this lab.

Determine the maximum voltage of the DC power supply you will use. (ie, 30 Volts)

[math] P =I^2R = \frac{V^2}{R}\lt 1/4 [/math] Watt
[math] \Rightarrow R \gt \frac{V^2}{1/4 Watt}=\frac{\left (30 V \right)^2}{1/4 \mbox{Watt}} = 3600 \Omega[/math]
By keeping your resistance values above 3600 [math]\Omega[/math] you should be able to avoid burning up 1/4 Watt resistors when your max voltage is 30 Volts.

The next objective is to use resistors which allow currents that you can measure with your voltmeter.

Since [math]V=IR \Rightarrow I = V/R = 30 \mbox{Volts}/3600 \Omega = 8\mbox{mA}[/math]

Determine the range of currents which the voltmeter can measure. (ie 1 mA)

To get measurable currents you need low resistance BUT the lower resistances will need to have a high power rating. These two competing properties limit the range of resistances you can use.


Select the three resistors you should use for this experiment.

Construct the circuit below

TF EIM Lab1.png


Enter the values of the DC voltage and Resisters that you used.

Use a voltmeter to measure the potential difference and resistances.

Variable Measured Value
[math]V_A [/math]
[math]R_1[/math]
[math]R_2[/math]
[math]R_3[/math]

Enter the measured and predicted quantities in the table below

Given [math]V_A[/math] and the values of all resistors, use Kirchoff's laws to calculate BY HAND the

a.) Predict the value of [math]V_B[/math]

b.) Predict the values of the three currents.

c.) compare your predictions and measurements by filling in the table below.

Variable Measured Value Predicted Value % Difference
[math]V_B[/math]
[math]I_1[/math]
[math]I_2[/math]
[math]I_3[/math]

Internal resistance (30 pnts)

Measure the internal resistance of a "D" cell battery by graphing the current on the x-axis and the measured voltage on the y-axis for several values of the resistance [math]R_L[/math] shown in the circuit below. Begin with [math]R_L = 1k\Omega[/math] and then decrease it by a factor of 5 for each subsequent measurement. You can use a volt meter to measure the current and potential difference.

TF EIM Lab1a fig.pngTF EIM Lab1b fig.png



R_{Load} ([math]\Omega[/math]) V (Volts) I (mA)
0.5
10
47
93
990


[math]V_A - V_B = IR_{Load} = V_{bb} - I R_{int}[/math]

[math](V_A - V_B) = - R_{int} I + V_{bb}[/math]

[math]y = mx+b \Rightarrow R_{int} =[/math] slope of V-vs- I plot

Questions (20 pnts)

  1. What conservation law is involved in Kirchoff's Loop Theorem?
  2. What does the slope in the internal resistance plot above represent?


Forest_Electronic_Instrumentation_and_Measurement

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