Series and Parallel Circuits i i2 i3 i = i1 +i2 + i3

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```Ver. 1.2
Series and Parallel Circuits
In this experiment we will investigate the properties of several resistors connected in series and
parallel. Our purpose is to verify the simple equations for the equivalent resistance (Req) in series and
parallel connections, and to verify the current relations when a potential is placed across a network
(circuit) connecting resistors in series or parallel with each other.
Resistors are said to be in series if each terminal end of a resistor is connected to a terminal
end of another resistor such that only one path for the passage of electrical charges (current) exists. The
diagram below shows three resistors connected in series.
i
R1
i
R2
i
R3
i
Since only one path exists, any charge q passing through the network must pass through each resistor.
Therefore the current i ( =Δq/Δt) will be the same through all the resistors. In this experiment we will
check this property. Now since Ohm’s Law tells us the current - potential relationship is given by
V = iR
The voltage across the series network of resistors should be the sum of the individual voltage drops
across the resistors or
Vtot = iR1 + iR2 + iR3 + etc.
Vtot = i(R1 + R2 + R3 + etc.) = i(ΣRi)
If we factor out the common term i, the equivalent resistance becomes ΣRi. That is, the effective
resistance is the resistance that would allow the same current to flow and would have the same
potential across it as Vtot.
Req = R1 + R2 + R3 + etc.
Several resistors are said to be in parallel if each one represents an independent path for the
transfer of charges between two points The diagram below shows three resistors connected in parallel
across a potential V.
i
V
i1
i2
i3
R1
R2
R3
From Ohm’s Law we know that the current through each resistor depends on the value of the
resistance and the potential difference across the resistor. When a charge q leaves the potential source,
a fraction q1 passes through resistor R1, another fraction q2 passes through R2 and the remaining
charge q3 passes through R3 . Conservation of electrical charge implies: q = q1 + q2 + q3 . Therefore
in a time interval Δt the currents satisfy the relationship:
q/Δt = (q1 + q2 + q3)/ Δt = q1/Δt + q2/Δt + q3/Δt
i = i1 + i2 + i 3
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Now because all the resistors are in parallel the potential (voltage) difference across each of them is the
same so that Ohm’s Law gives us:
R1i1 = V
Therefore
or
R2i2 = V
i = i1 + i2 + i3 = V/R1 + V/R2 + V/R3
R3i3 = V
=
V(1/R1 + 1/R2 + 1/R3)
=
V/Req
1/Req = 1/R1 + 1/R2 + 1/R3
when we have a parallel configuration.
PROCEDURE:
1.) Series connections properties. Select three resistors, 1000 Ω, 1500 Ω and 3300 Ω and
using the ohmmeter measure their actual resistance using the DVM. Now connect them in series in
the circuit shown in the diagram below. Use the DC power supply output on the blue box to supply
a 20V across the series connection. The circuit diagram labels A, B, C, and D represent parts of the
circuit where we wish to measure the current in the circuit. In order to measure the current
“flowing” through the circuit an ammeter must be inserted at each of these points. Your lab
instructor will show you how to connect the ammeter at each point in order to measure the current.
CIRCUIT DIAGRAM
A
B
C
R1
R2
R3
DC +
supply
D
BLOCK DIAGRAM
A
DC +
supply
-
R1
B
R2
C
R3
V
D
Our goal here is to verify the current is the same at each point in a series circuit. In general the
procedure consists of these steps :
1. Set the function to A (for ammeter), and the range of your DVM ammeter at 1 A.
2. Break the circuit at A, B, C or D by disconnecting one at a time, the wire that
connects the resistors and adding a wire to the second resistor. The wire closest to
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the potential source is put into the ammeter input on the DVM, and the second wire
in inserted into the COM.
3. Now apply the power to the circuit and lower the range scale to an appropriate value.
Once you have completed your measurements of the currents, you can move onto the voltage
(potential difference) measurements. In this part of the experiment you will measure the potential
difference across each resistor and the potential difference across the entire circuit. In general the
procedure consists of these steps :
1. Set your DVM to the DC voltage, and the range to the highest available.
2. Set the probes of the DVM across the voltage source and record the voltage of the
supply.
3. Now place the probes across each resistor and record its potential drop. Lower the
range scale to a more sensitive range if necessary.
2.) Parallel connections properties. Using the same three resistors, connect them in parallel in
the circuit shown in the diagram below. Again use the DC power supply output on the blue box to
supply a 20V across the series connection. The circuit diagrams labels A, B, C, D and E show five
locations in the circuit where we wish to measure the current. Again in order to measure the current
“flowing” through the circuit an ammeter must be inserted at each of these points.
CIRCUIT DIAGRAM
A
itot
i1
DC +
supply
-
i2
R1
E
i3
R2
R3
B
C
D
i1
i2
i3
R1
R2
R3
B
C
D
itot
BLOCK DIAGRAM
itot
A
DC +
supply
itot
E
Our goal here is to verify how the currents divide in a parallel circuit. In general the procedure
consists of the same steps :
1. Set the function to A (for ammeter), and the range of your DVM ammeter at 1 A.
2. Break the circuit at A, B, C, D or E by disconnecting the wire that connects the
resistors and adding a wire to the second resistor. The wire closest to the potential
source is put into the ammeter input on the DVM, and the second wire in inserted
into the COM.
3. Now apply the power to the circuit and lower the range scale to an appropriate value.
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Once you have completed your measurements of the currents, you can move onto the voltage
(potential difference) measurements. In the case of the parallel connection we expect the voltage
to be the same across each resistor, verify that this is true.
1. Set your DVM to the DC voltage, and the range to the highest available.
2. Set the probes of the DVM across the voltage source and record the voltage of the
supply.
3. Now place the probes across each resistor and record its potential drop. Lower the
range scale to more sensitive range if necessary.
PRESENTATION:
Series Connection
Verify:
Vtot = iR1 + iR2 + iR3 + etc. = V1 + V2 + V3 + etc.
Req = R1 + R2 + R3 + etc.
do this by calculating Req and calculating i.
Parallel Connection
Verify:
i = i1 + i2 + i 3
i1 = V/R1
i2 = V/R2
1/Req = 1/R1 + 1/R2 + 1/R3
i3 = V/ R3
do this by calculating Req and calculating i.
ERROR ANALYSIS: The usual considerations regarding agreement of theoretical and experimental
numbers. Also comment on errors due to the calibration of the meters.
CONCLUSION: Draw some conclusions about how well we verified the rules for series and parallel
circuits.
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DATA SHEET
RESISTORS:
R1
R2
Ω
&plusmn;
R3
Ω
&plusmn;
&plusmn;
SERIES CONNECTION:
iA
Vtot
iB
VR1
iC
VR2
iD
VR3
PARALLEL CONNECTION:
itot A
Vsupply
i1
VR1
i2
VR2
i3
VR3
itot E
64
Ω
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