Download Parallel Resistance

BASIC ELECTRICAL
Parallel Resistance
OBJECTIVES
Define Parallel Connection
Define Parallel Circuit
Calculate Parallel Resistive Circuit
INTRODUCTION
We have worked with Series Connections as one way to connect loads together to make a circuit, in this
lesson we will discuss another way to connect loads together called Parallel Connections. This lesson will cover
parallel resistive connections, parallel resistive circuits, and calculating total resistance for a parallel resistive
circuit.
Parallel Connection
A parallel connection is defined as anytime two electrical components are connected so that there is
more than one path for current through the two components. (See Figure 1 for examples of parallel connections.)
Look at the Schematic Diagram View, if Current enters at 1 and
travels to the right through the two resistors it will have to leave at 2 .
There are multiple paths (two in this case) through the two resistors,
this is what is called a Parallel connection.
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1
2
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Figure 1
Schematic Diagram
Physical Layout
Breadboard Layout
Parallel connections can be made be adding more than just two electrical components together. There
can be many paths that divide up the initial current and share the same voltage. A good example would be the
electrical system of an automobile in which the 12 V battery’s Voltage is made common throughout the vehicle,
to the starter, to the radio, to the lights, and anything else that needs the electrical pressure to do work. Though
there is one Voltage source (the battery) there are multiple paths; a different path through each of the components mentioned. (See Figure 2 for an example of multiple resistors in a parallel connection.)
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R1
R1
R2
R2
R3
R3
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Figure 2
Schematic Diagram
Physical Layout
Breadboard Layout
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Alternate Circuits with 2 Parallel Resistive Paths
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2
Parallel Circuit
As stated in the “Series Resistance Lesson” , resistive connections are typically the “LOAD” of an
electrical circuit. To make a complete electrical circuit we need to add the rest of the components of a circuit.
Remember an electrical circuit had four main parts, the source, the circuit path, the load, and the control. The
parallel connection we have discussed so far represents the Load and what type of path the circuit is. Figure 3
shows the rest of the components that make up a Parallel Circuit. These examples have three components in the
“LOAD”.
SW1
R1
R2
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R1 R2 R3
R3
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Schematic Diagram of Series Circuit
B1
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B1
SW1
Physical Diagram of Series Circuit
SW1 in the Physical Diagrams is a SPDT but is being
used as a SPST as in the schematic diagram, this is OK
to do.
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Figure 3
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R1 R2 R3
Physical Diagram of Parallel Circuit built on Breadboard
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Calculate Parallel Resistive Circuit
The resistive value of a parallel circuit can look at as if it was just one total resistance. This means the
parallel circuit may have R1, R2, and R3, but these resistances can be looked at as one “Total Resistance”.
There are several ways the total resistance can be calculated for a parallel circuit. Figure 4 shows the formula
for a circuit that has just two parallel resistances.
Figure 4
R1 x R2 = Rt
R1 + R2
Formula for resolving two resistances into Rt
Example 1
200 Ω
200 Ω
200 x 200
40000
=
200 + 200
400
= 100 Ω
Two 200Ω Resistors would look like a single 100Ω Resistor to the rest of the circuit.
100 Ω
Notice that the color for the first strip on the resistor has changed. In the
electronic component lesson these color bands or strips will be explained, it
should be noted know that the resistance is as labeled. (100 Ω)
The formula in figure 4 can only be used to solve for two resistances at a time. This does not mean that
the formula cannot be used to solve for circuits that have more than two parallel resistances. However,
it does mean that to solve for more than two resistances in parallel you would need to solve for two
resistances at a time using the formula and then use the formula again for the next two resistances, and
so on until the circuit is down to just one resistance (Rt). This is shown in Figure 5.
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Solve for these
two reisitors
as in Figure 4.
Then redraw
the circuit to
see what is left
to solve for.
200 Ω
200 Ω
200 Ω
R1
R2
R3
200 Ω
R4
200 x 200
40000
=
200 + 200
400
= 100 Ω
Two 200Ω Resistors would look like a single 100Ω Resistor to the rest of the circuit.
In the second
step you can
solve for any
two of the
remaining three
resistors.
200 Ω
200 Ω
R1
R2
The 100 Ω Resistor
shown is not really there,
R3 and R4 are still in
the circuit. The 100 Ω
resistor shown is just the
mathematical equivalant
of the the two. We have
NOT changed he original
circuit.
100 Ω
200 x 200
40000
=
200 + 200
400
= 100 Ω
Two 200Ω Resistors would look like a single 100Ω Resistor to the rest of the circuit.
In the final step
in this example
select the two
remaining resistance values.
100 Ω
100 Ω
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100 x 100
10000
=
100 + 100
200
= 50 Ω
Two 100Ω Resistors would look like a single 50Ω Resistor to the rest of the circuit.
Since there is just one
resistance left this is Rt.
The above steps can be a long process for a circuit that has many parallel paths, also inaccuracies because of rounding can build up. So, is there a different way to calculate parallel resistances that can deal with
these issues? Yes there is, but at first glance this formula may look harder than the previous way shown, believe
me it is not. See figure 5.
1
1
1
1
1
+
+
+
=
R1 R2 R3 ••• Rn Rt
Figure 5
Using a calculator, this one formula can solve for any number of resistances in parallel. (Notice the ...
Rn) This formula can be changed to another useful formula by taking the reciprocal of (that is inverting) both
sides of the formula. See figure 6.
1
Rt =
1
1
1
1
+
+
+
R1 R2 R3 ••• Rn
Figure 6
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The way to perform the calculations in figure 6 uses the X-1 or 1/X button on your calculator. Follow the
steps in figure 7 for the circuit shown.
R1
R2
��X
200 Ω
200 Ω
200 Ω
200 Ω
R1
R2
R3
R4
R3
��X
��X
R4
��X
��X
200
��X
��X
For this example
200
200
��X
200
��X
��X
The calculator should show 50 Ω
Figure 7
The Example below shows a schematic diagram version of the simplification process.
SW1
SW1
B1
200 Ω
400 Ω
400 Ω
R1
R2
R3
B1
Circuit 1
200
��X
100 Ω
Rt
Circuit 2
400
��X
400
��X
��X
The calculator should show 100 Ω
The battery and the switch would not see a difference between circuit 1 and circuit 2, it is said
that R1, R2, and R3 are equivalent (equal) to Rt. In the following lessons being able to simplify a circuit to its total resistance will be very important.
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