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Ohm 1
RESISTANCE & OHM’S LAW (PART I and II) – 8-MAC Objectives:
To understand the relationship between applied voltage and current in a resistor
and to verify Ohm‟s Law.
To understand the relationship between applied voltage and current in a Light
Emitting Diode (LED).
To understand simple parallel and series circuits and to use this understanding to
determine the circuit connections of a hidden “black box” resistor network.
To test the connection between resistance, current, voltage, and power dissipation.
Equipment: Digital multi-meters(2 per group)(DMM for short), variable power supply
(prefer 0 -18 Volt), snap-on-circuit-board, 6V lamps, resistors, LED's of different colors.
A multi-meter is a device that can be used as a voltmeter, an ammeter, or an ohmmeter.
Background: Electric resistance, R, is defined by:
R = V / I , (1)
where V is the potential difference (or voltage drop) across the resistor and I is the current
through it. The unit of resistance is the Ohm. ( = Volt/Ampere = V/A). If R = 0 in a
circuit, it is called a "shorted" circuit; if R = ∞, it is called an “open” circuit.
The product P = I V is the power dissipated in the resistor
(of course P = I V = I 2 R = V2 / R ).
Ohm's Law: For many materials resistance R is a constant, independent of I and V. The linear
relationship between V and I, V = I R is called Ohm‟s Law. Materials obeying Ohm‟s
Law are said to be "Ohmic" materials. (Simple light bulbs do NOT satisfy this Law,
manufactured resistors do. An LED does NOT obey Ohm‟s Law. )
Equivalent Resistance: When several resistors are connected together, they can also be
replaced with a single resistor that will have the same potential drop and draw the same
total current as the combination of resistors. This resistance is called the “equivalent
resistance ” Req” of the circuit.
Resistors in Series:
Figure 1. Series Connections
When the same current flows through each of a number of resistors, they are said to be in
series. The equivalent resistance Req for resistors connected in series is
Ohm 2
i
iR
eqR (2)
Note that here Req is larger than any of the individual resistances.
Resistors in Parallel
Figure 2. Parallel Connections
When the same potential difference appears across each of a number of resistors, they are
said to be in parallel. The equivalent resistance Req for resistors connected in parallel is
i iReqR
11 (3)
Note that here Req is smaller than any of the individual resistances.
Electrical Measurements:
A voltmeter is a device to measure the potential drop across a circuit or across part of a
circuit. The voltmeter itself has a very large resistance so that the current through it is
negligible, and it can be assumed that the potential drop across the resistor in Fig. 3a is
the same whether or not the voltmeter is attached. A voltmeter is always connected in
parallel with the circuit element whose potential difference is to be measured.
An ammeter is a device to measure the current through a circuit element. The ammeter
itself has a very small resistance so that the potential drop across is negligible, and it can
be assumed that the current through the resistor in Fig. 3b is the same whether or not the
ammeter is inserted in the circuit. An ammeter is always connected in series with
circuit element whose current is to be measured.
If you do not connect the ammeter the correct way, you can severely damage the device.
Ohm 3
Figure 3a Voltmeter Connection Figure 3b Ammeter Connection
An ohmmeter is a device that measures resistance. It is connected in parallel across the
resistance to measured. You should NEVER measure the resistance of a resistor that is
still part of a circuit. You will probably destroy the ohm-meter, certainly you will
measure the wrong resistance. In practice first disconnect all leads of the resistor to be
measured, so no electric current runs through the resistor, except for the current supplied
by the battery inside the ohm-meter itself.
If you do not connect the Ohmmeter the right way, you can severely damage the device.
PART I
Diagnostic Phase: You should always make a schematic drawing on paper before building any circuit!
Make a simple circuit on the snap-on-circuit-board, consisting of three 6V lamps in
series and a variable power supply. Start at low power output and slowly turn up the
power until the lamps start to glow.
Voltage.
Switch the multi-meter to the Voltage Mode (V=) and measure the total voltage
difference over the entire circuit. The two leads are connected to the meter through the
two right outlets. Subsequently also measure the voltage drop over each lamp.
Current,
Interupt the circuit and reconnect but insert also the leads of the multimeter, switch the
multi-meter to the Ampere Mode (A=). The two leads are connected to the right and left
outlet of the meter. You now measure the electric current flowing out of the power
supply, through the circuit and through each lamp.
Since by now you have become an expert in electric circuits, put the lamps back in the
box and let‟s start with the serious stuff.
Activity 1: Ohms' Law. You will measure the resistance of an unknown resistor in three ways and test if Ohm‟s
Law applies:
Ohm 4
A. (Easy way): Use an ohmmeter to measure the resistance. See if the measured
resistance remains the same if the leads to the ohmmeter are reversed.
B. (Fancy but more realistic way): Connect an ammeter in series with the resistor
and a voltmeter in parallel with it as shown below in figure 4, i.e. use two multi-meters in
the circuit. Use a variable output power supply to drive the circuit. As the output voltage
is increased, measure I and V for a dozen values of V.
To determine the resistance R and verify the linear relation of Ohm‟s Law, use Logger
Pro and plot I versus V for a number of different voltage settings, make a linear fit to the
data and obtain the correlation coefficient. From the slope you can obtain the resistance
R. How?
Figure 4. Measuring voltage and current simultaneously of an Ohmic resistor.
C. (Way for dummies): Read the commercial color coding of the resistor. Does it
agree with A and B?
Activity 2: Light emitting diode(LED) - NON-Ohmic behavior.
As an example of a device which does not obey Ohm's law, you will investigate an LED
(Light Emitting Diode).
For a NON-Ohmic device there is no „easy way‟ to measure its resistance with an ohm-
meter. Actually its resistance is not fixed, but an I versus V plot will show its response
to an applied voltage.
A. Make a circuit by connecting a 100 ~ 200 ohm resistor in series with an LED.
A
V
+
Ohm 5
See figure 5. The resistor is put in the circuit to prevent burning out the LED.
Connect a voltmeter across the resistor and measure the voltage across the resistor
for several values of the supply voltage setting. (Keep the Voltage to be less than
5V and the current below 10 mA to prevent damage to the LED).
Since Vpower source = Vps is known, and Vresistor + VLED = Vps , VLED can be determined.
Of course an alternative is to measure VLED directly. To measure the current I you can
add an ammeter to the circuit as you did in Activity 1.
At what values of the current does the LED start to emit light, and at which values does it
not emit light?
Now reverse the leads from the power supply and repeat the measurement of current in
the same range of voltage setting. Compare your observations with what you would
expect for Ohmic behavior.
B. Try another diode with a different color.
( Different materials have different electron energy gaps. As the electrons jump the gap
this leads to emission of light of different colors. Available are LED‟s which emit red,
green, yellow, or blue light.)
resistor
v oltmeter
LED
v oltage supply
Figure 5. Measuring voltage and current for non-Ohmic device.
PART II
Activity 3: Back to Ohmic resistors. For this activity you will use three resistors -- two with the same resistance and one with
a different resistance (10 k10 kand 20 kfor example).
A. Determine all possible ways you can connect the resistors in series and/or parallel
to give different equivalent resistances. Draw a diagram of each of these combinations,
and calculate the theoretical equivalent resistance.
B. Set up two of the circuits in A on the breadboard and measure the actual equivalent
resistance with a ohmmeter and compare with your calculation.
Ohm 6
C. Calculate the power dissipated by each resistor in the two circuits in B if a 12 V
power supply is connected across the circuit.
Appendix: Resistors are coded with 4 colored stripes around the body of the resistor that allow easy
determination of the resistance. The code for the first 3 colored bands is given below:
RESISTOR COLOR CODES
COLOR 1ST DIGIT 2ND DIGIT MULTIPLIER
Silver ....................... ........................ ................................. 10-2
Gold ......................... ........................ ................................. 10-1
Black ....................... ........................ 0 ............................... 100
Brown ...................... 1 ...................... 1 ............................... 101
Red .......................... 2 ...................... 2 ............................... 102
Orange ..................... 3 ...................... 3 ............................... 103
Yellow ..................... 4 ...................... 4 ............................... 104
Green ....................... 5 ...................... 5 ............................... 105
Blue ......................... 6 ...................... 6 ............................... 106
Violet ....................... 7 ...................... 7 ............................... 107
Gray ......................... 8 ...................... 8 ............................... 108
White ....................... 9 ...................... 9 ............................... 109
The 4-th colored band gives the "tolerance," i. e., the uncertainty in the marked resistance, as follows:
gold: 5% silver: 10% no color: 20%
Example:
Figure 8. A Color Coded Resistor
Helpful Hint: Most people who get incorrect results in this experiment do so because they
fail to use the multi-meter correctly. Make sure the multi-meter is reading ohms AND
that the gain or sensitivity is at the maximum number of significant digits for that
resistance. Change the sensitivity by trial and error the maximum number of digits.
Ohm 7
RESISTANCE & OHM’S LAW (preliminary questions)
Names: _________________________________________________ Section: _______
You have three identical light bulbs each with a constant (assume Ohmic) resistance of
150 . Suppose you connect the circuits to a 12 V battery.
a.) Draw diagrams showing all the 4 possible ways they can be connected in series or
parallel or in a combination of series and parallel.
b.) You can identify brightness with Power (= Energy per second) .
How is the current I passing through each bulb related to the brightness?
c.) Which of the circuits is the brightest, and which circuit is the dimmest?
Ohm 8
Report -- RESISTANCE & OHM’S LAW (Part I)
Name: _________________________________________________ Section: _________
Partners: _______________________________________________Date: ____________
Part I
Diagnostic Phase, building a circuit:
On the snap-on-circuit-board construct a simple circuit of three 6V lightbulbs in series
and connections to the variable power supply.
Starting at low voltage, slowly turn up the voltage output of the power supply until the
lamps start to glow. DO NOT GO HIGHER.
Put the multi-meter on DC Volts (V=, not V~) and measure the total voltage over the
three lamps. [WITHIN THE DC-VOLT RANGES ON THE MULTI-METER ALWAYS
START WITH THE HIGHEST RANGE. If the reading is too low, turn to a lower range.]
Now measure the voltage drop over each lamp.
Put the multi-meter on DC Ampere [again start at highest range] and measure the electric
current that flows out of the power supply. (In order to do this step, you have to interrupt
the circuit and insert the leads of the Amp-meter). If you do not follow this step
carefully, you may damage the multi-meter.
Measure the current in between lamp 1 and lamp 2.
Make a schematic drawing of the circuit, showing lamps, power supply and connecting
wires.
Mark the values of your measured voltages and currents in the circuit. Indicate direction
of the current and + and – for voltages.
Ohm 9
Activity 1:
Determine an unknown resistance in three ways (a, b, c) and verifying
Ohm’s Law.
a.) Direct from Ohm-meter: reading = Runknown = _____________ ______
Note that the resistor Runknown at this point should be „free-standing‟ (not part of any
circuit). If you do not disconnect the resistor from the circuit, you may damage the
multi-meter.
b.) From I versus V graph:
Draw a circuit of the unknown resistor and the power supply, and indicate where in this
circuit you measure the current I and the voltage V .
Construct the circuit you have just drawn.
Include leads to the power supply, leads to the voltmeter, and leads to the current meter.
In this circuit vary the output voltage of the power supply and measure voltage and
current at least for 12 settings in the range 0 – 18 V, (measure the voltage V over R and
the current I passing through R).
V (V) I(mA) V (V) I(mA) V (V) I(mA) V (V) I(mA)
Make a graphical representation ( V on horizontal axis, I on vertical axis ) and include the
graph with the report. (Don’t forget labeling the axes and give it an appropriate title).
Ohm 10
How is the slope of a linear fit related to the resistance R? Do not forget the units.
Runknown = ______________ ____
Verify Ohmic behavior by checking if your data agree with Ohm’s Law, i.e. how good
is your linear fit.
correlation =______________.
c.) Resistance determined for the same unknown resistor from the color code:
Runknown = _______________ ____ ± _______
The manufacturer’s claimed tolerance is indicated by the last color band on the right.
Is your measured value in the tolerance range given by the manufacturer?
Ohm 11
Activity 2: Light emitting diode (LED) - non-Ohmic behavior.
[Do not allow more than 10 mA of current to flow through the LED to
prevent damage.]
A. Draw a circuit connecting a red LED in series with a 100 ~ 200 Ohm resistor
connected to the power source. Where in this circuit do you measure voltage V
over the LED and where do you measure current I passing through the LED?
(For simplicity, measure the voltage directly over the LED.)
B. Construct this circuit on the snap-on-circuit-board.
Measure I and VLED for a range 0 – 5 V allowing only small increments in the
current I and record in the table below.
C. The value of current I when the red LED first lights up: ________________mA
D. The value of the voltage over the red LED, VLED when the LED first lights up:
____________V
Describe your observations that show I versus V behavior of the LED.
Include a table of I versus VLED for the range 0 – 5 V for again at least 12 settings. Since
current I may change rapidly, aim at steps of at most 0.5 mA for the current. Keep the
current below 5.0 mA. Remember I-max = 10 mA!!! LED’s are delicate and only
allow low currents. In addition, show several data points (steps of about 0.2 mA) just above the voltage
where the LED starts lighting up and the current is still small.
What happens if you reverse the leads of the LED? (rotate the LED 180 degrees, leave
everything else unchanged).
Ohm 12
VLED (V) I (mA) VLED (V) I (mA) VLED (V) I (mA) VLED (V) I (mA)
Make a graph showing I versus VLED (current vertical, voltage horizontal). Include also
the data for reversed leads in the same graph by extending the voltage axis to include also
negative values. (Reversed is equivalent to negative voltage.)
Include the graph in the final report.
How is this non-Ohmic behavior different from Ohmic behavior?
Comment on the several aspects of the behaviour shown in the graph.
Ohm 13
Report -- RESISTANCE & OHM’S LAW (Part II)
Name: _________________________________________________ Section: _________
Partners: _______________________________________________Date: ____________
PART II
Activity 3: Resistance combinations.
Use the ohmmeter to measure the resistances of the three resistors you will use. Choose
two of the resistances to be as closely the same value as possible and the other resistance
to be at least twice as big.
R1 = ___________ ____ R2 = ___________ ____ R3 = ___________ ____
A. Draw diagrams of all possible ways that you can connect these three resistances in
series and/or parallel to give different equivalent resistances. For each diagram calculate
the theoretical equivalent resistance (show your work)
B. Set up two of the circuits and measure the actual value with an ohmmeter.
C. Calculate the power dissipated by each resistor in the two circuits in B if a 12 V
battery is connected across the circuit. [Not all entries are needed to be filled.]
Circuit 1 Req (theoretical) = ______________ ___
Req (experimental) = ______________ ___
Power dissipated = ______________ ___
diagram work
Circuit 2 Req (theoretical) = ______________ ___
Req (experimental) = ______________ ___
Ohm 14
Power dissipated = ______________ ___
diagram work
Circuit 3 Req (theoretical) = ______________ ___
Req (experimental) = ______________ ___
Power dissipated = ______________ ___
diagram work
Circuit 4 Req (theoretical) = ______________ ___
Req (experimental) = ______________ ___
Power dissipated = ______________ ___
diagram work
Ohm 15
Circuit 5 Req (theoretical) = ______________ ___
Req (experimental) = ______________ ___
Power dissipated = ______________ ___
diagram work
