Physics 261
Simple Series Resistor Circuits
Resistors
Resistors come in many shapes and forms, related to power capacity, precision, and cost. This lab
will employ low-cost, carbon composite resistors.
Resistor power ratings are roughly proportional to the dimensions of the resistors. The low
voltages employed in these experiments should permit the use of even small (7 mm long x 2-3 mm
diameter), 1/4W capacity resistors. But to check, recall that
P = IV = I 2 R =
V2
.
R
If your rough calculation shows you near the limit of a small resistor, use a larger sized one.
Nominal values of resistors (determined by the manufacturer based on the carbon mixture used
in construction) are usually indicated on the outside of the resistor by a color coding [see Figure 1].
Such coding gives resistance (in Ohms) in scientific notation: nm × 10k , where n is the number
associated with the colored band closest to an end of the resistor, m is the number associated with
the next colored band, and k is the number associated with the third colored band. See Table 1 for
the color coding values. The precision with which the resistor was manufactured is indicated with
Figure 1: A carbon-composite resistor with colored bands indicating nominal value and precision.
Table 1: Resistor color codes
black
0
green
brown 1
blue
red
2
violet
orange 3
gray
yellow 4
white
5
6
7
8
9
a fourth band: if absent or colored brown, the precision is ±20%; if silver, the precision is ±10%;
and if gold, the precision is ±5%.
Multimeter
The TENMA 72-7720 multimeter, which you will use in this investigation, measures voltage, current,
resistance, and capacitance, and tests diodes. The rotary switch sets what is to be measured or tested
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and, more specifically, the range of values. The smallest setting above the maximum possible value
should always be chosen, so as to get the greatest possible precision.
Of the four available input plugs, common (COM, black) is used for all voltage, current, and
resistance measurements, and, in general, is connected to the (relatively) negative probe (direct
current, DC) or the one closest ground (alternating current, AC), while the other three are connected to the (relatively) positive probe (DC) or the one farthest from ground (AC). Capacitance
is measured between the microAmp positive input and the voltage-resistance positive input. The
upper right plug rightmost plug, labeled VΩDiode, is obviously used for voltage (voltmeter) and
resistance (ohmmeter), and to test a diode. The remaining two plugs (other than COM) are for
current (ammeter). The one labeled µA mA is for low currents, while the one labeled 20A MAX is
for higher currents.
Note that there’s an ON/OFF button, labeled POWER, and a HOLD button for taking a snapshot of a varying measurement.
It is important to remember that (special circumstances excepted), the ammeter (current), because its input impedence is so low, must be in series with circuit segment you are measuring, while
the voltmeter, due to its very high input impedence, must be in parallel.
Precision Each setting of the multimeter has an intrinsic precision, the specifications of which
are provided by the manufacturer, and reproduced in the tables below. (Recall from the capacitor
investigation writeup how to use the information in these tables; be sure to keep all of these tables
available whenever you are required to use a multimeter).
Range
200 mV
2V
20 V
200 V
1000 V
Table 2: DC Voltage; Input Impedence: 10 MΩ
Resolution
Precision
Overload Protection
100 µV
±(0.5% + 1 lsd)
250 VDC or AC rms
1 mV
±(0.5% + 1 lsd) 1000 VDC or 750 V AC rms
10 mV
±(0.5% + 1 lsd) 1000 VDC or 750 V AC rms
100 mV
±(0.5% + 1 lsd) 1000 VDC or 750 V AC rms
1V
±(0.8% + 2 lsd) 1000 VDC or 750 V AC rms
Table 3: AC Voltage; Input Impedence: 10 MΩ; Frequency Response: 40 Hz ∼ 400 Hz; Mean value
response to a sine wave
Range
Resolution
Precision
Overload Protection
200 mV
100 µV
±(1.2% + 3 lsd)
250 VDC or AC rms
2V
1 mV
±(0.8% + 3 lsd) 1000 VDC or 750 V AC rms
20 V
10 mV
±(0.8% + 3 lsd) 1000 VDC or 750 V AC rms
200 V
100 mV
±(0.8% + 3 lsd) 1000 VDC or 750 V AC rms
1000 V
1V
±(1.2% + 3 lsd) 1000 VDC or 750 V AC rms
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Table 4: DC Current; Measurement Voltage Drop: Full range at 200 mV
Range
Resolution
Precision
Overload Protection
20 µA
0.01 µA
±(0.8% + 1 lsd) 0.5A, 250 V fast-type fuse
2 mA
1 µA
±(0.8% + 1 lsd) 0.5A, 250 V fast-type fuse
200 mA
100 µA
±(1.5% + 1 lsd) 0.5A, 250 V fast-type fuse
20 A
10 mA
±(2% + 5 lsd)
Un-fused
Table 5: AC Current; Measurement Voltage Drop: Full
Hz ∼ 400 Hz; Mean value response to a sine wave
Range
Resolution
Precision
200 µA
0.1 µA
±(1% + 3 lsd)
2 mA
1 µA
±(1% + 3 lsd)
200 mA
100 µA
±(1.8% + 3 lsd)
20 A
10 mA
±(3% + 5 lsd)
range at 200 mV; Frequency Response: 40
Overload Protection
0.5A, 250 V fast-type fuse
0.5A, 250 V fast-type fuse
0.5A, 250 V fast-type fuse
Un-fused
Ohm’s Law Test: Simple Series Circuit
• Select a 5.1 kΩ resistor and a 10 kΩ resistor. Note its color sequence and its nominal precision.
• Measure the resistance of each resistor and note the readings along with the uncertainties. Do
the measurements and nominal values agree? Justify quantitatively.
• Calculate the total resistance of the two resistors in series (using the measured values); propagate uncertainties.
• Set up the following circuit.
200 Ω
2 kΩ
20 kΩ
200 kΩ
2 MΩ
20 MΩ
200 MΩ
0.1 Ω
1Ω
10 Ω
100 Ω
1 kΩ
10 kΩ
100 kΩ
Table 6: Resistance
±(0.8% + 3 lsd)
±(0.8% + 1 lsd)
±(0.8% + 1 lsd)
±(0.8% + 1 lsd)
±(0.8% + 1 lsd)
±(1% + 2 lsd)
±[5%(reading − 10) + 10 lsd]
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250
250
250
250
250
250
250
VDC
VDC
VDC
VDC
VDC
VDC
VDC
or
or
or
or
or
or
or
AC
AC
AC
AC
AC
AC
AC
rms
rms
rms
rms
rms
rms
rms
• Varying voltages from 1V to 10 V, record voltmeter and ammeter readings (don’t worry about
uncertainties).
• Noting (think about it) which values correspond to dependent and independent variables, check
whether your data verify the (appropriate) form of Ohm’s Law.
• Check that the coefficient as determined from the intercept of the regression matches that
expected from your earlier calculation, modified, if necessary, by the form of Ohm’s Law
(again, this requires thought) you are testing.
• In conclusion, is Ohm’s Law satisfied by this simple series circuit?
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