Download 4 Series Circuit Characteristics

UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE
Department of Electrical and Computer Engineering
Experiment No. 4 - Series Circuit Characteristics
Overview:
This experiment will have the student verify Ohm’s law by comparing measured data with
calculated data. Then the student will investigate the characteristics of series circuits and the
voltage divider rule for these circuits.
Ohm’s law relationships:
In this section some basic information about circuits will be mentioned. A circuit is a path for
electrons to flow through. The path is from a power sources negative terminal, through the
various components and on to the positive terminal. Although the physical picture of current is a
flow of electrons, in engineering and science conventional current flow is used. Conventional
current is the flow of positive charge, and electron flow can be modeled as a flow of positive
charge in the reverse direction. The reason for this dilemma is that much of the literature in
circuits was written before the true nature of current was understood.
Think of it as a circle. The paths may split off here and there but they always form a line from
the negative to positive.
NOTE: Negatively charged electrons in a conductor are attracted to the positive side of the
power source.
Voltage is the electrical force, or “pressure”, that causes current to flow in a circuit. It is
measured in VOLTS (V or E).
Current is the movement of electrical charge - the flow of electrons through the electronic
circuit; however, we will think of it as a flow of positive charge from the positive terminal
through the circuit and returning to the negative terminal. Current, I, is measured in AMPERES
(AMPS, A).
Resistance is anything that causes an opposition to the flow of current in a circuit. It is used to
control the amount of voltage and/or amperage in a circuit. Everything in the circuit causes a
resistance (even wire). It is measured in OHMS ( ).
The three forms of Ohm’s Law are: I=E/R, E=IR and R=E/I
All we really need to know is E = IR. With the use of algebra the other forms are easily obtained.
When comparing measured data with calculated data, you should allow for a reasonable
tolerance in your data. For example: Assume the measured voltage is 15 V while the calculated
voltage is14.8 V. To compare these, we will calculate the % error, defined as
Percent error = [(measured value – calculated value)/calculated value]*100%
For the above values we have
percent error =
15V − 14.8V
100 % = +l.4 %
14.8V
Due to the accuracy of the measurement instruments (digital voltmeter, digital ohmmeter about
+l%~ analog ammeter about ±3%), measurements in the DC laboratory that agree within ±5%
may be considered equal for most practical purposes.
Series circuits:
A series circuit is one with all the loads in a row, like links in a chain. There is only ONE path
for the electricity to flow. If this circuit was a string of light bulbs, and one blew out, the
remaining bulbs would turn off.
In this lab-session the student will verify experimentally, using measured and calculated values,
the following series circuit rules:
a.
b.
c.
Total circuit resistance equals the sum of the individual resistances.
The current is the same at all points in a series circuit.
The sum of the voltage drops equals the source voltage.
Voltage divider rule for series circuits:
In any given series circuit, the current that flows through each circuit element (resistors and
voltage source) is the same. If fixed resistors (not variable resistors) are used, then the voltage
drops will be fixed and will be directly proportional to the ratio of the resistor sizes. If a
reference point is established (usually called “common” or “ground) it is then possible to
measure the voltage at all other points in the circuit, with respect to this “common” point. If the
“common” point is then relocated to another point in the circuit, the voltage (measured with
respect to the common point) at each other point will be different. This common point is usually
chosen as ground.
The ratio of resistance values in a series circuit determines the ratio of voltage drops. Therefore,
given the source voltage and the value of each resistor, the voltage drops can be found by
expressing ratios of voltage to resistance:
Vsource = V1
Rtotal R1
Vsource = V2
Rtotal R2
Note: this is just Ohm’s Law: I=V/R, where I is constant
If the equations above are solved for the voltage drops:
V1=Vsource [R1/Rtotal] and V2=Vsource [R2/Rtotal]
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This is called the VOLTAGE DIVIDER RULE.
Stated in words, “The voltage across a resistor is a fraction of the total voltage, and that fraction
is one whose numerator is that RESISTANCE, and whose denominator is the TOTAL
RESISTANCE.”
Conversely, the size of a resistor can be determined when given the total resistance, source
voltage and desired voltage drop:
R1=Rtotal [V1/Vsource]
Using the above expression, the student will design a voltage divider to supply various voltages
with respect to “common” for a given source voltage, a group of resistors, and the values of
desired voltages.
Also, the above relationship can be developed by a current based argument. The current in a
series circuit is the same for all elements and is given by Vsource / Rtotal . The voltage across the
resistor R1 is simply R1I or V1 = R1 Vsource / Rtotal , and this expression can be rearranged to give
the above expression for R1.
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Pre Lab – Series Circuit Characteristics
1. Use the voltage divider rule (VDR) developed in procedure 1:
a. For the circuit in Figure 2B, calculate (using the VDR) the voltage at each point,
A, B, C, D and E with respect to ground. Record the calculations below and refer
to them in your lab report.
Voltage
A
B
C
D
E
Figure 2B
Figure 2C
Figure 2D
Figure 2E
b. In the same manner, repeat step 1a for each of the other circuits 2C, 2D and 2E.
2. Designing a voltage divider:
Refer to the circuit in Figure 3. R1, R2, R3 and R4 are 1.2kΩ, 5.6kΩ, 3.3kΩ and
9.1kΩ resistors, but not in that order. Using the VDR in the form that solves for
resistance (R) rather than voltage (V), solve for the necessary resistor placements (or
locations) that will result in the voltages as shown. Record below the resistor value you
determined for:
R1 = __________
R2 = __________
R3 = __________
R4 = __________
RT = __________
(INSTRUCTOR’S SIGNATURE_____________________________DATE______________)
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Lab Session — Series Circuit Characteristics
PART ONE: Total resistance in a series circuit.
1. Show your pre-lab work to the instructor at the beginning of the lab session
2. Measure each individual resistor and record below.
R1 = __________
R2 = __________
R3 = __________
R4 = __________
R5 = __________
R6 = __________
3. Connect the circuit in Figure 1 with the voltage source removed and replaced by the Ohm
meter.
4. Measure the total resistance. Rtotal =_______________
PART TWO: Current relationship in a series circuit.
1. Connect the circuit in Figure 1, measure, and record the current at nodes a, b, c, d, e, f,
and g. To measure the current through a node, break the circuit at that node and remake
the circuit by inserting the ammeter or handheld at that node. The ammeter must be
connected in such a way that circuit current will be forced to flow through the meter.
Ia =__________________
Ib =__________________
Ic =__________________
Id =__________________
Ie =__________________
If =__________________
Ig =__________________
INSTRUCTOR'
S INITIALS
DATE:
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PART THREE: Verifying voltages in the circuit.
1. Verify by measurement, the voltages between various points in a series circuit:
a. Connect the circuit in Figure 1.
b. Measure and record below the voltage drop across each resistor. When measuring
VAB, the voltmeter probe should be connected to point A and the common lead to
point B. This would be expressed as VAB. Note that in the subscript “AB”, the
first letter “A” is the point to which the probe is connected and the second letter
“B” is the point to which the common lead is connected. Therefore, the
expression VAB means the voltage at point “A” with respect to point “B”.
VR1 = VAB = __________
VR2 = VBC = __________
VR3 = VCD = __________
VR4 = VDE = __________
VR5 = VEF = __________
VR6 = VFG = __________
c.
Properly label these measured voltage drops on each resistor in Figure 1. Mark
the polarity (use a + and a - to indicate polarity) of the voltage drop on each
resistor.
d.
Measure the voltage, VCE, which is the voltage at point C with respect to point E.
When measuring, the voltmeter probe should be connected to point C and the
common lead to point E. Note that in the subscript “CE”, the first letter “C” is the
point to which the probe is connected and the second letter “E” is the point to
which the common lead is connected.
VCE ____________
Does VCD + VDE = VCE?
INSTRUCTOR'
S INITIALS
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e.
In a like manner, measure and record the following:
VAC = ___________ VCA = ___________ (note opposite polarity!)
VDG = ___________ VEA = ___________
VBF = ___________ VCG = ___________
2. Measuring Voltage with respect to ground:
a. Connect the circuit in figure 2A.
b. Measure and record the voltage drop across each resistor.
Recall that the probe is connected to the first subscripted
node, and the common is connected to the second
subscripted node.
VAB = VR1 = __________
VBC = VR2 = __________
VCD = VR3 = __________
VDE = VR4 = __________
Properly label these measured voltage drops on each resistor
in Figure 2A. Mark the polarity (use a + and – to indicate
polarity) of the voltage drop on each resistor.
c. Connect the common lead of the DMM to ground, which is point E. With the DMM
probe, measure and record the voltage at each of the points A, B, C, D, and E. A
voltage listed with a single subscripted variable means that voltage is measured with
respect to ground.
VA = __________ VB = __________ VC = __________ VD = __________
VE = __________
NOTE: According to Kirchhoff’s voltage law, VB = VDE + VCD + VBC = VBE. Do your
measured values from 2.b and 2.c show that VB = VDE + VCD + VBC?
d. Refer to circuit 2B below, with ground at point D. Measure the voltage at all points
(A, B, C, D, E) with respect to this new reference point. Record the measured voltage
at each point on the circuit diagram 2B.
INSTRUCTOR'
S INITIALS
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e. Repeat step 2.d above, three times: for Figures 2C, 2D and 2E.
Be sure to move the reference point (ground) to agree with the schematic, in each case.
Record the results on Figures 2C, 2D and 2E.
3. Designing a voltage divider:
a. Measure the voltage at points A, B, C and D. Record.
VA = __________
VB = __________
VC = __________
VD = __________
9.94 V
INSTRUCTOR'
S INITIALS
DATE:
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Post Lab - Series Circuit Characteristics
1. Add the measured values of R1, R2, R3, R4, R5, and R6 recorded in step 1 of the procedures.
Record the total.
2. Perform a computer simulation of the circuit in Figure 3 using PSpice, and use the results to
verify Pre lab resistor value placement. Print the simulation with voltages, and submit it with
this report. (On Mosaic machines: click START -> All Programs -> MOSAIC XP ->
Engineering -> Electrical -> Cadence Pspice -> Capture CIS ->New Project -> Choose
“Analog or Mixed A/D” radio button)
For help and information on Pspice:
A PSpice User’s Guide link is provided on the ECE Laboratory Website.
2. What conclusions can be made from the results of the procedures 1-3?
3. Noting the relationship between the voltages measured between two points and the indicated
individual voltage drops labeled on each resistor in Figure 1. Explain how the voltage
between two points could be predicted prior to actually measuring with the DMM.
4. Explain how to determine the location of the 5.6 kΩ resistor in the voltage divider of Figure
3.
5. Explain how to determine the resistance size required in any voltage divider, when you are
given the data in the same manner presented above.
6. What conclusions can be made from the results of the procedures in part two?
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