name____________________ period _______ lab partners___________________________________
Electrical Resistance and Ohm's Law
Introduction
This lab is built around two questions: 1) "What does the resistance of a wire depend on? and 2) "How are
voltage, current, and resistance in a simple circuit related?" The following chart provides some basic information with respect to these quantities (including connecting with analogy between flow of charge vs. water)
Quantity, symbol
Description
Unit
Calculate using this:
Water Analogy
Voltage or Potential
Difference, V
A measure of the Energy
difference per unit charge
between two points in a
circuit.
Volt (V)
V=IR
(the voltage drop form
of Ohm's Law)
Water Pressure
Current, I
A measure of the flow of
charge in a circuit per unit
time
Ampere (A)
I=V/R
(the current drawn form
of Ohm's Law)
Amount of water
flowing per unit time
Resistance, R
A measure of how
difficult it is for current to
flow in a circuit.
Ohm ()
R=V/I
A measure of how
difficult it is for water to
flow through a pipe.
Resistance is present in three places in electric circuits: 1) in wires, 2) in electric circuit components--most
notably discrete resistors, and 3) in electrical loads (appliances, light bulbs, etc.). Part I of the lab involves
measuring the resistance of wires of a) the same cross-sectional area A but different length L, b) the same
length L but different cross-sectional area A, and c) and d) different material and therefore having a different
resistivity ρ. Resistivity has units of ohms times meters ( Ω m) The lower a material's resistivity, the higher
its conductivity. Excellent conductors like silver and copper have the lowest values of resistivity; carbon--a
so-called semi-conductor typically has values 20,000 times greater. In Part I you'll use equation #1 below (or
a hypotheses based on it) to compute resistivity. In Part II you'll start by a) measuring the resistance of
discrete carbon resistors. You'll then involve these resistors in investigating b) how current varies with
voltage provided the resistance is held constant, and c) how current varies with resistance provided the
voltage is held constant.
Figure #1--circuit for Part II b, c
Objectives / Overview
1) to provide experience using a digital multimeter to
measure resistance and current.
2) to get practice using the resistor color codes to
determine specified resistance value and tolerance
3) to make measurements in an effort to verify
R = ρ L / A. (equation #1)
4) to make measurements in an effort to verify
I = V / R. (equation #2)
Materials
DC power supply (for part I)
carbon resistors on board (part II)
nickel / silver, copper wires on spools (part I)
resistor color band decoder wheel
digital multimeter (parts I and II)
connecting wires, electrical leads (part II)
carbon rod, metric ruler to measure (part I)
CAUTION: electrical shock hazard--take precautions as suggested by instructor!
Procedure Note: Record your measurements in the appropriate table in the Data section.
Part I a) Follow your instructor's directions and use the multimeter as an ohmmeter to measure the resistance of these different lengths of #30 nickel / silver wire: 40 cm, 80 cm, 120 cm, 160 cm, 200 cm.
b) Repeat the above step for #28 nickel / silver wire of length = 200 cm
c) Repeat the above step for #30 copper wire of length = 2000 cm
d) Repeat the above step for the carbon rod. Measure the latter's length and diameter using the metric ruler.
Part II a) Use multimeter as ohmmeter to measure the resistance of resistors A, B, C, D, E, F on the board.
Using the colors of the bands on these resistors, determine the resistance, Ω & tolerance in % of each.
b) Hookup up the circuit pictured in Fig. #1 with the multimeter configured as ammeter to measure current.
Note the resistor you use will be the one closest to 400 Ω, and the DC voltmeter is built into the DC power
supply. Do not turn on the power supply until your hookup is approved by the instructor. Turn on the
power supply, and measure the current for DC voltages of 0, 2.5, 5.0, 7.5, 10.0, 12.5, and 15.0 volts.
c) Using the circuit of Fig. #1 with the DC voltage=5.0 volts, measure the current through each resistor A-F.
Data
Part I a) The resistance of different lengths of #30 nickel / silver wire.
length
40 cm
80 cm
120 cm
resistance, Ω
160 cm
200 cm
Part I b) The resistance of different cross-sectional areas of same length (200 cm) of nickel / silver wire.
#28 nickel / silver wire
#30 nickel / silver wire
resistance, Ω
Part I c) The resistance of wires of same different cross-sectional area, prorated* to have same length (200
cm) but made of different materials: copper vs. nickel / silver
#30 copper wire, 2000cm #30 copper wire, 200 cm
#30 nickel / silver wire, 200 cm
resistance, Ω
* note: divide the entry for #30 copper wire, 2000cm by 10 to get entry for #30 copper wire, 200 cm
Part I d) The resistance of the carbon rod of length =____cm and diameter =____cm is measured as ____ Ω
Part II a) The resistance values--as specified and measured--of carbon resistors on the resistor board.
resistor letter color bands
resistance, Ω & tolerance based on code measured resistance, Ω
A
B
C
D
E
F
Part II b) For resistor = ____ Ω, the following currents were measured when the voltage was set as follows:
voltage, V
0 volts
2.5 volts
5.0 volts
7.5 volts
10.0 volts
12.5 volts
15.0 volts
current, mA
Part II c) With voltage set at____volts, the following currents were measured for the resistor indicated:
resistor, Ω A=
Ω B=
Ω
C=
Ω
D=
Ω
E=
Ω F=
current, mA
1 / R, ohm-1
Ω
Data Handling / Questions
1) Using Data in Part Ia, with your calculator (TI 83, etc.) enter (STAT, EDIT) length L of wire in meters in
List 1 and resistance R in ohms in List 2. Do a linear regression (STAT, CALC ) and record the equation for
the best fit line when the calculator plots L horizontally vs. R (vertically). Record slope (a in y= ax + b)
and correlation coefficient. Does your data support the hypothesis R ~ L (with ρ and A constant)? Discuss.
2) The slope of your best fit line in 1) above = the resistivity ρ of the nickel-silver alloy divided by the crosssectional area A30 of the #30 wire = 5.09752 x 10-8 m2. So multiply your slope by A30 to get ρ.
How does your value for the resistivity ρ of the nickel-silver alloy compare with the expected value?
Compute % error.
3) Using the Data in Part Ib, and the ratio of the cross-sectional areas of the #30 wire and #28 wire, that is
A30 / A28 = (r30 / r28)2, test the hypothesis that R ~ 1 / A (with ρ and L constant). Note: #30 gauge wire is
smaller in area than #28: r30 = 0.0127381 cm and r28 = 0.0160528 cm. Compute % difference between what
the theoretical hypothesis predicts and what your measured resistances yield.
4) Using your Data in Part Ic (after you've prorated the resistance of the #30 gauge copper wire so that its
value is equivalent to what would be expected for a wire 1/10 of the length), test the hypothesis that
R ~ ρ (with A and L constant). To do this, use the accepted values for resistivities of the nickel-silver alloy
and copper as provided by your instructor. Compute the % difference between what the theoretical
hypothesis predicts and what your measured resistances yield.
5) BONUS: Using your Data in Part Id and R = ρ L / A. (equation #1) determine the resistivity of carbon in
the form used in the rod. Compare your result with the resistivity of a conductor like copper--show your
work. Based on this comparison, explain why carbon is considered a semi-conductor.
6) Using your Data in Part IIa and comparing measured resistances with resistance values specified by the
resistor's color code--decide which resistors' measured values are outside limits suggested by the tolerance.
Results of this investigation: resistors outside limits are: A B C D E F none of them (circle letters)
provide a sample calculation for a particular resistor to show how you decided:
7) Using Data in Part IIb, with your calculator (TI 83, TI 84, etc.) enter (STAT, EDIT) voltage V in volts in
List 1 and current I in amps in List 2. Do a linear regression (STAT, CALC ) and record equation for the
best fit line when the calculator plots V horizontally vs. I (vertically). Record slope (a in y= ax + b) and
correlation coefficient. Does your data support the hypothesis I ~ V (with R constant)? Discuss.
8) If I = V / R (equation #2) is valid, the slope of your best fit line in 7) above should = 1 / R. Does it?
Compute % error and discuss.
9) Using values for R in the table for Data Part IIc, compute the inverse of R--that is 1 / R. On the graph
paper provided, construct a graph of 1 / R (plotted horizontally, in ohm-1) vs. current I (vertically, in amps).
Draw a best fit line through your points. (Optionally, do this with Logger Pro, print out graph and attach.)
10) Using Data in Part IIc, with your calculator (TI 83, TI 84, etc.) enter (STAT, EDIT) 1 / R (in inverse
ohms) in List 1 and current I in amps in List 2. Do a linear regression (STAT, CALC ) and record equation
for the best fit line when the calculator plots 1 / R horizontally vs. I (vertically). Record slope (a in y= ax +
b) and correlation coefficient. Does your data support the hypothesis I ~ 1 / R (with V constant)? Discuss.
11) If I = V / R (equation #2) is valid, the slope of your best fit line in 10) above should = V. Does it?
Compute % error and discuss.