Download Intro to Physics Lab

GateWay CC
The Basics of
Resistance Measurements
PHY101 Physics Lab:
Introduction:
The objectives of this lab are to familiarize students with the principles of test instruments for
measuring voltage, current and resistance.
In this experiment, you will verify a single resistance that is equivalent to a group of resistances
connected in series, parallel, and series/parallel. You will be familiar with operation of an
ohmmeter and learn how to hook-up electrical circuit.
Equivalent Resistance
Resistors can be connected in series or in parallel in electric circuits. When resistors are
connected in series, they share the same current, and the voltages across them add to give the
total voltage. The opposite is true in parallel resistance circuits; that is, parallel components
share the same voltage, and their currents add to give the total current.
The equivalent resistances of a series and a parallel circuit as shown in Figure 1can be calculated
using the following formulas. These illustrate the case involving four resistors.
Req ( series)  R1  R2  R3  R4
Req( parallel) 
R1
(1)
1
(2)
1
1
1
1



R1 R2 R3 R 4
R2
R3
R4
Req
R1
R2
R3
R4
Req
Figure 1
Procedure:
gatewaycc – resistance measurement.doc
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GateWay CC
1. Resistance Measurement
Get the following four resistors: 10, 50, 100, and 500. Measure the resistance with
the digital multimeter using the two-wire method. Record the nominal and the measured
values in the table shown below. Calculate the percentage difference between the nominal
and actual value. Use the given formula to calculate the % difference
Measured Difference(%) 
Nominal Value  Measured Value
Measured Value
Does the difference fall within the tolerance?
Resistor
Nominal
Value ()
1
10
2
50
3
100
4
500
Measured
Value ()
Measured
Difference
(%)
Comment
2. Resistance circuits measurements
Calculate the value of the equivalent resistance for each of the circuits shown in Figures 2
and 3. Show your calculations and enter your result in the space provided.
Set up each circuit as shown in the diagrams, and measure the equivalent resistance using
multimeter. Please build the circuit as neat as possible. Record your measurements in the
space provided.
Calculate the percent error for each case.
Series connections
Requivalent (calculated ) = _______ 
Requivalent (measured ) = _______ 
Percent error
= _______%
Requivalent (calculated ) = _______ 
Requivalent (measured ) = _______ 
Percent error
= _______%
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GateWay CC
Requivalent (calculated ) = _______ 
Requivalent (measured ) = _______ 
Percent error
= _______%
Figure 2: Series connections of resistors
Parallel connections
Requivalent (calculated ) = _______ 
Requivalent (measured ) = _______ 
Percent error
= _______%
Requivalent (calculated ) = _______ 
Requivalent (measured ) = _______ 
Percent error
= _______%
Requivalent (calculated ) = _______ 
Requivalent (measured ) = _______ 
Percent error
= _______%
Figure 3: Parallel connections of resistors
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GateWay CC
Questions
1.
How many paths for current to flow in the series circuit?
2.
What happens to the total resistance as you add resistors in series? Increased,
decreased, stays the same? Why?
3.
How many paths are there for current to flow in a parallel circuit?
4.
What happens to the total resistance as you add resistors in parallel? Increased,
decreased, stays the same? Why?
5.
Prove this statement: The total resistance of parallel resistors is always less than that
of the smallest resistor. This proof can be shown by doing the calculation for the
following circuits:
a. A parallel circuit with three resistors: 10 ohms, 20 ohms, and 30 ohms. The total
resistance should be less the 10 ohms.
b. A parallel circuit with three 100 ohms resistors and one 5 ohm resistor. The total
resistance should be less the 5 ohms.
3. Measurement of resistance using the Ohm’s Law
Ohm’s law states that electric current (I) through the resistor depends linearly on the voltage
(V) applied across the resistor:
R
V
I
Quantity R in Ohm’s law formula is electric resistance measured in Ohm’s
To verify Ohm’s law – or to measure the resistance, two quantities need to be measured:
Voltage across the resistor and current through the resistor. Voltage is measured using
multimeter in Volts mode. The current is measured using analog ampere-meter. The circuit
used to perform these measurements is shown in figure 4.
Figure 4. Ohm’s Law verification
Connect the elements of the circuit using 6 V battery. Record the voltage and current reading on
the chart bellow. Replace one of the two resistors with 50 , 100 , and 500  values and each
time record the voltage and current data on the table.
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GateWay CC
Calculate the resistance using the Ohm’s law:
Rcalc 
V
I
Calculate the absolute difference between the nominal and calculated value:
Absolute Difference  Nominal Value  Calculated Value
Calculate the percentage Difference between the nominal and calculated value:
Absolute Difference 
Nominal Value  Calculated Value
100%
Calculated Value
Record the Voltage and Current readings in the table bellow
Resistor
Nominal
Calculated
Value of
Voltage (V) Current (A) Resistance
the
()
Resistor()
1
10
2
50
3
100
4
500
Absolute
Difference
()
Percentage
Difference
(%)
.
Questions:
1. Assume that you have two 100  resistors, but need 50  resistor. Is there a way to
connect 100  resistors to get 50 . Explain.
2. Calculate the total resistance of three resistors connected as shown.
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