L3. Electric Circuits
Tuesday, May 23, 2017
1:29 PM
Purpose
In this experiment you will examine the resistive behaviour of three different devices – a standard resistor (a device
designed to have a specific resistance), a light emitting diode (LED), and a light bulb.
Prelab Checklist
Prelab Quiz
Review Breadboards document
Intro Video(s)
Theory
The resistance R of a circuit element through which current is flowing is defined by
R = V/I
Equation 1
where R is the resistance (in ohms), I is the current through the device (in amps), and
V is the voltage or potential difference (in volts) between the ends of the device.
Plotting the current through a device as a function of voltage across the device yields information about the resistive
behaviour of the device. A straight line relationship implies the device has a constant resistance that is independent
of current – these devices are known as ohmic devices. A non-linear relationship implies that the resistance varies
with current; these devices are known as non-ohmic devices. Metals at a constant temperature and moderate
currents are ohmic devices, while semiconductor devices are good examples of non-ohmic devices. Resistance also
changes with temperature – it increases with temperature for most materials except semiconductors where it
decreases with temperature.
Equipment Supplied
You are supplied with the following: 1 variable power supply, 1 bread board (read the Breadboard document on
OnQ for information on bread boards), 2 digital multimeters, an unknown resistor, 2 LEDs (light emitting diodes),
resistors to limit current (1 390high wattage resistor, 1 100high wattage resistor) and a variety of wires.
A multimeter can be used as either an ammeter or a voltmeter. To measure the current though a device such as a
resistor, an ammeter is placed in series with the device as shown in Figure 1(a). To measure the voltage across a
device, a voltmeter is placed in parallel with the device, as shown in Figure 1(b). For this experiment assume that
the meters are ideal, i.e.:
- Ideal ammeters have zero resistance, and therefore cause no voltage drop in the circuit.
- Ideal voltmeters have infinite resistance, and therefore draw no current from the circuit.
Figure 1(a) and 1(b)
(note: prior to this lab you may review sections on resistors in your physics textbook)
L3. Electric Circuits Page 1
To set up the multimeters follow the steps below before you switch the meter on:
As an AMMETER
As a VOLTMETER
Apparatus and Procedure
A circuit for measuring the resistance of a ‘device under test’ is shown in Figure 2.
L3. Electric Circuits Page 2
A circuit for measuring the resistance of a ‘device under test’ is shown in Figure 2.
Figure 2a: Circuit diagram with device under test
Figure 2b: Circuit image matching Figure 2a, replacing the device under test with an LED
Rp is a protection resistor which is used to limit current to the device under test. If the current to the device is too large then
the device will be damaged, often called "burned out".
The green ‘ground’ connection from the power supply should be connected to the ‘ground’ on the breadboard.
You can easily reverse the direction of the current flow by switching the connections to the power supply.
Safety Note: Make sure your TA checks your circuit before you switch anything on. As you are taking
readings the circuitry will start to heat up. Be careful touching the circuit after it has been on, it may be HOT.
Since you do not initially know the relationship between current and voltage for a particular device it is important to
plot the data during the experiment. In regions where the graph is changing rapidly it is necessary to collect more
data points to adequately characterize the device.
1. Study of a resistor
Set up the circuit as shown in Figure 2 with the “unknown” resistor as the "device under test" and the 390 
resistor as the protection resistor Rp (for 390 the first 3 lines are orange, white and brown)*.
*You can identify resistors by the colour code of the lines. The first two lines represent the numerical value.
The third line represents the multiplier. A possible forth line indicates the tolerance
Based on the power rating of the resistor under test you can safely take readings up to 1 V. Before you start
collecting data adjust the scales on each meter so that you use the smallest scale possible while being able to
read the largest value you will get. The numbers on the scale buttons indicate the largest reading for that scale.
Using the smallest possible scale will reduce the error you obtain because the error in the meter reading is a
percent of the reading plus ‘one’ least significant digit (LSD) – for a value displayed as 10.03V “1 LSD”=
L3. Electric Circuits Page 3
percent of the reading plus ‘one’ least significant digit (LSD) – for a value displayed as 10.03V “1 LSD”=
0.01V . For a given voltage (or current) the LSD depends on the scale selected. The smaller the scale the
smaller the LSD will be, but you need to make sure the scale will allow you to read your largest value. The
voltmeter error is +/- (0.1%of the reading + 1 LSD). The ammeter error is +/- (0.3%of the reading + 1 LSD).
Using the general voltmeter and ammeter error equations above along with your meter settings, write
down the equation you will use to calculate the meter errors.
δV =
δI =
0.0005 Volts
0.00005 Amps
(algebraic expression in terms of voltage)
(algebraic expression in terms of current)
Create a blank scatter plot in Excel before you start taking data and select the current column as the vertical
axis and the voltage column and the horizontal axis. Doing this will allow you to visualize data as you go.
Take about six sets of voltage and current readings, varying the voltage across the unknown resistor from 0 -1 V
using the power supply. Obtain six more data points with negative voltage values by switching the leads to the
power supply. Changes in the voltage between readings should be roughly equal. Record your data into Table
1 in Sheet1 of the Excel Spreadsheet provided. Ensure your current readings are reported in amps (A), not
milli-amps (mA). If your data does not produce a linear graph, as expected for an ohmic device, you have
made a mistake and should check with your TA before proceeding.
Fill the error columns using the equations you derived above and add error bars to your graph.
Use Trend Line to plot the linear regression line (line of best fit) on the graph. Include the equation with V and
I rather than x and y (e.g I=3V+5).
Table 1: Raw data modeling the current as a function of voltage for a resistor
Voltage across device
V [V]
Error in voltage δV
[±V]
Current through device
I [A]
Error in current δI
[±A]
0.293
0.0005
0.0132
0.00005
0.347
0.0005
0.0157
0.00005
0.410
0.0005
0.0186
0.00005
0.563
0.0005
0.0256
0.00005
0.664
0.0005
0.0303
0.00005
0.713
0.0005
0.0325
0.00005
0.812
0.0005
0.0370
0.00005
-0.142
0.0005
-0.0064
0.00005
-0.259
0.0005
-0.0118
0.00005
-0.480
0.0005
-0.0219
0.00005
-0.575
0.0005
-0.0263
0.00005
-0.674
0.0005
-0.0307
0.00005
-0.857
0.0005
-0.0391
0.00005
-0.990
0.0005
-0.0452
0.00005
L3. Electric Circuits Page 4
There are error bars however they are very small
Figure 3: Current as a function of voltage for a resistor
Conduct a regression analysis to determine the error in the slope and intercept and to produce a graph of the
residuals. Paste the residual plot below and report the value and error of your slope m.
Figure 4: Residual plot of current as a function of voltage for a resistor
m=
0.04558 ±
0.00003
.
Write out an expression for the slope m of your I vs. V plot. To start, rearrange
(Equation 1) to be in the
form
that will match your graph then write out an algebraic expression for the slope m.
m=
(algebraic expression)
Rearrange this expression to solve for R in terms of your slope value m.
R=
(algebraic expression as a function of the slope)
For this example the Matlab script will not be necessary to calculate error as it is a trivial one variable
calculation. Apply the general error equation
to determine δR:
δR =
(algebraic expression as a function of the slope and δslope)
L3. Electric Circuits Page 5
Now plug in your values into your equation for R and δR to calculate the final answer for the resistance of the
'unknown resistor'
δR =
R=
±
0.01

± 0.01444  = 21.94 ± 0.01 
2. Study of LEDs
In this case the “device under test” is a series of 2 light emitting diodes ..
Figure 3: Circuit with LEDs
Use the same 390  resistor as the protection resistor Rp .
The longer 'leg' of the LED signifies the positive end of the device and the shorter 'leg' signifies the negative
end.
Ensure you use two LEDs of the same colour. Record your LEDs colour's above the caption for Table 2(a)
below.
Before you start collecting data readjust the scales on each meter so that you use the smallest scale possible
while being able to read the largest value you will get. The manufacturer's current limit through the LEDs
is stated as 20mA (ammeter reading) so do not exceed this. Check what voltage this corresponds with.
Reminder: The voltmeter error is ± (0.1%of the reading + 1 LSD). The ammeter error is ± (0.3%of the
reading + 1 LSD).
Using this information along with your new meter settings, write down the equation you will use to
calculate the meter errors.
δV =
δI =
0.005 Volts (algebraic expression in terms of voltage)
0.00005 Amps
(algebraic expression in terms of current)
Repeat the procedure from the previous section, creating a blank scatter plot and recording the data into Table
2(a) in Sheet2 (take about 10 readings once the current starts to flow). Ensure your current readings are
reported in amps (A), not milli-amps (mA). This time include only positive voltages.
LED colour:
RED
.
Table 2(a): Raw data modeling the current as a function of voltage for an LED
Voltage across device
V [V]
Error in voltage δV
[±V]
Current through device
I [A]
Error in current δI
[±A]
1.17
0.005
0.0000
0.00005
2.11
0.005
0.0000
0.00005
3.29
0.005
0.0007
0.00005
L3. Electric Circuits Page 6
3.29
0.005
0.0007
0.00005
3.43
0.005
0.0026
0.00005
3.60
0.005
0.0070
0.00005
3.73
0.005
0.0114
0.00005
3.80
0.005
0.0144
0.00005
3.90
0.005
0.0188
0.00005
4.00
0.005
0.0233
0.00005
4.20
0.005
0.0320
0.00005
In this case, the graph will not be a straight line so the data points should NOT be evenly spaced. At low
voltages there will be no current, then at some point after a certain ‘cut in’ voltage you will begin to get marked
increases in current. Make sure that you took enough readings in the vicinity of this change to define it well.
We want to determine the cut-in voltage (the voltage where the LEDs switch ‘on’). There are many ways to do
this, but we will choose to determine the line of best fit through the points that are of the linear section of the
graph (AKA clearly above the cut in), and estimate of the cut-in voltage as the value of V when I=0 for this
equation. Start by plotting the line of best fit for the data above the cut in and include the equation in the form
I = mV + b
Figure 6: Current as a function of voltage for an LED
Starting with the equation I = mV + b determine the algebraic expression for Vcut in (the value of V when I=0).
Vcut in =
3.474 volts
(algebraic expression as a function of the slope and intercept)
Perform a regression on the linear data to determine the error on your slope m and intercept b. Report both
values and their respective errors below.
m=
0.0440 ±
0.0002 .
b=
-0.1529 ± 0.0008 .
Use the Matlab Uncertainty script to calculate the value of Vcut in and Vcut in. Include the Sensitivity Analysis
plot below.
L3. Electric Circuits Page 7
Figure 7: Histogram plot of uncertainty contributions from each variable
Vcut in =
3.48
±
0.02 .
What do you think the cut-in voltage for 1 LED would be?
Since in series the voltages are added to find the total voltage, the voltage across 1
LED would be half that of the 2 LEDS.
V1 LED= 3.48/2 = 1.74 volts
What happens if the current is reversed? Switch the leads on the power supply to find out. The negative
lead of the power supply should now go to the short 'leg' of the LEDs.
LEDs only emit light when current goes in 1 direction. The voltage will be
negative but the current will not go through.
3. Final Question
You have two plots of current vs. voltage. Describe the significant features of each and compare them.
How does the resistance vary with current for each device? What happens when you reverse the current
direction (by changing from a positive voltage across the device to a negative voltage)?
In the first graph, the voltage vs current relationship is very linear and goes into
the 3rd quadrant. It also has a y-int of y=0. In the other graph, there needs to be
an initial voltage that needs to be reached for the current to start passing
through. The 2nd graph has an x-int which signifies the initial voltage and it also
doesn’t go into the negative quadrants because of the nature of LEDs.
The resistance in the first device was very linear as shown in the trendline which
means it is an ohmic resistor. The LED's resistance decreased as voltage
increased which is shown by the initial values on the graph being concave up
which means it is a non-ohmic resistor.
L3. Electric Circuits Page 8
NOW GO TO “FILE” AND CLICK EXPORT. UNDER 1. EXPORT CURRENT: SELECT PAGE AND UNDER 2. SELECT FORMAT
SELECT PDF. UPLOAD YOUR PDF FILE TO THE ONQ DROPBOX. DO NOT UPLOAD THE ONENOTE FILE TO THE DROPBOX.
L3. Electric Circuits Page 9