Parallel Circuits
Types of Circuits: Parallel
A parallel circuit can be constructed by connecting light bulbs in such
a manner that there are SEVERAL PATHS for charge flow (CURRENT);
the light bulbs are placed within a separate branch line, and a
charge moving through the circuit will pass through only
one of the branches during its path back to the low potential
(negative) terminal of the battery.
Since there is now several current paths, the total current of the
circuit equals the sum of the current in each branch.
I = I1 + I2 + I3
Types of Circuits: Parallel
Does this hold true?
I = I1 + I2 + I3
Let’s take a closer
look at how the
current is flowing
through each branch.
12 A
9A
3A
9A
6A
6A
3A
6A
3A
3A
12 A
9A
9A
6A
6A
Types of Circuits: Parallel
Let’s look at
voltage:
Each branch is hooked up to the same battery.
Each branch has the same voltage (electric pressure).
V = V 1 = V 2 = V3
Outlets in a house are connected in parallel so you can
use one appliance without having to turn them all on.
Types of Circuits: Parallel
Let’s look at
RESISTANCE:
The actual amount of current always varies inversely with
the amount of overall resistance.
I=V
Req
1= 1 + 1 + 1
Req R1
R2
R3
Types of Circuits: Parallel
The total resistance of a parallel circuit is a fraction
of all of the resistors added together!!!!
1= 1 + 1 + 1
Req R1
R2
R3
Types of Circuits: Parallel
I=V
Req
So the more resistors you add in parallel the lower the
equivalent resistance will be. And because Req  the I 
sometimes to a potentially dangerous level.
This is why we have circuit breakers or fuses inserted into
the main line of our homes. When we are trying to use too
many electrical devices (resistors) in parallel the current gets
to be too much and a fuse in blown.
http://phet.colorado.edu/sims/ohms-law/ohms-law_en.html
Inside the fuse is a small piece of metal,
across which current must pass. During
normal flow of current, the fuse allows the
current to pass unobstructed. But during
an unsafe overload, the small piece of
metal melts, stopping the flow of current.
Circuit breakers are switches that are
tripped when the current flow passes a
unsafe limit. The excess of current
typically triggers an electromagnet,
which trips the circuit breaker when an
unsafe limit is reached. Once tripped,
the switches simply turn off. That stops
the flow of electricity, which will remain
off until the switch is reset.
Parallel Summary:
I = I 1 + I2 + I3
V = V1 = V 2 = V 3
1= 1 + 1 + 1
Req R1
R2
R3
In this animation you should notice the
following things:
•More current flows through the smaller
resistance. (More charges take the
easiest path.)
•The battery or source is represented by
an escalator which raises charges to a
higher level of energy.
•As the charges move through the
resistors (represented by the paddle
wheels) they do work on the resistor and
as a result, they lose electrical energy.
•By the time each charge makes it back to
the battery, it has lost all the electrical
energy given to it by the battery.
•The total of the potential drops ( potential difference) of each "branch" or
path is the same as the potential rise ( +
potential difference) across the battery.
This demonstrates that a charge can only
do as much work as was done on it by the
battery.
•The charges are positive so this is a
representation of conventional current
(the apparent flow of positive charges)
•The charges are only flowing in one
direction so this would be considered
direct current ( D.C. ).
30 Ω
10 Ω
Series vs. Parallel
Series
I
Parallel
I = I1 = I2 = I3
I = I1 + I2 + I3
V = V1 + V 2 + V3
V = V1 = V2 = V3
The more resistors
you have the less
the equivalent
resistance is, and
current increases.
Voltage never
changes.
V
R
Req
1= 1 + 1 + 1
= R1 + R 2 + R3 R
R1
R2
R3
eq
The more resistors you have the more the equivalent
resistance is, and current never changes. The voltage across
each resistor adds up to the total voltage of the source (battery).
Hooking up Devices Properly
Ammeters, because of the way they are built, have very
little resistance. So they can be placed in series with
other devices in a circuit and not disrupt the current.
It would be just like putting a low resistor in the circuit.
A
A
If you placed an ammeter in parallel you would never be
able to measure the total current of a circuit because
parallel branches don’t have the same current as the
total current of the circuit.
Hooking up Devices Properly
Voltmeters on the other hand have a very high resistance
and when placed in series would disrupt the current so they
are placed in parallel within the circuit- in a separate branch.
V
V
Also, think about what a voltmeter is measuring…the
potential difference ACROSS a resistor or a battery.
The device needs to be places ACROSS a resistor or battery.
Try this…
4Ω
12 V
Calculate (a) the equivalent
resistance, (b) the potential
difference across each resistor,
and (c) the current through
each resistor.
I = I1 + I2 + I3
V = V 1 = V 2 = V3
6Ω
12 Ω
a. 1 = 1 + 1 + 1
Req R1
R2
R3
1= 1 + 1 + 1
Req R1
R2
R3
1= 1 + 1 + 1
Req 4 Ω 6 Ω 12 Ω
Need a common denominator
NOTE: Notice how the Req
is less than any of the resistors
1=
in the circuit.
Req
1= 3 +
Req 12 Ω
6
12 Ω
2 + 1
12 Ω 12 Ω
Req = 12 Ω
1
6
=2Ω
I1 = V
R1
I1 = 12 V
4Ω
I1 = 3 A
b. V = V1 = V2 = V3
V = 12 V
c.
I=V
R
12 V
4Ω
6Ω
I2 = V
R2
I2 = 12 V
6Ω
I2 = 2 A
I3 = V
R3
12 Ω I = 12 V
3
4Ω
I3 = 3 A
Try this…
A1
Find the magnitude of current
that is flowing through all
3 ammeters.
I = I1 + I2 + I3
12 V
A2
10 Ω
15 Ω
A3
V = V 1 = V 2 = V3
1= 1 + 1 + 1
Req R1
R2
R3
A1 = I1 = V
R1
I1 = 12 V
10 Ω
I1 = 1.2 A
A2 = I2 = V
R2
I2 = 12 V
15 Ω
I2 = .8 A
A3 = I1+ I2
A3 =1.2A + .8A
A3 = 2 A
Which two of the resistor arrangements below have the
same equivalent resistance?
1Ω
1Ω
A
8Ω
B
8Ω
2Ω
2Ω
C
2Ω
D
2Ω
Which circuit below would have the lowest
voltmeter reading?
6V
6V
A
C
20 Ω
20 Ω
V
40 Ω
40 Ω
V
6V
6V
B
D
20 Ω
40 Ω
V
20 Ω
40 Ω
V
Arrange the schematic diagrams below in order
of increasing equivalent resistance.
1
2
3
4
Find the resistance of R3.
Req = 2 Ω
R1 = 6 Ω
R2 = 6 Ω
1= 1 + 1 + 1
Req R1
R2
R3
R3 = ?