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16.6 Parallel and Series Circuits
Possible Paths
• We are now going to look at the
different paths that you can set up for
electrons
• Depending on the path you provide, you
can control the work that electrons do
for you
Tracing electrons
• To better understand circuits, there is
one simple way to figure how they will
travel – which will determine how the
circuit works
• ELECTRONS TAKE THE SHORTEST PATH
TOWARDS THE END OF THE CIRCUIT
• ELECTRONS NEVER BACKTRACK
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battery. Likewise, the red electron will continue forward – if it
was to turn right, it would move back towards the NEGATIVE
POLE of the battery
Series and Parallel Circuits
• There are 2 basic types of circuits
• SERIES: there is only one possible path
for the electrons to travel
• PARALLEL: there are 2 or more possible
paths for electrons to travel
• This fact gives different properties to
series and parallel circuits
Series and Parallel circuits are like
roads
SERIES
PARALLEL
Notice:
• Series circuits provide a single path
• Parallel circuits provide multiple paths
• The number of cars that take a path
depend on how easy it is to take the
path (bigger the road, less traffic)
• Same with electrons – more electrons
will take the path with least resistance
– so current increases in those paths
Naming loads in circuits
•Resistors are numbered
RT
•Therefore:
R2
R1
•The voltage for R1 is
referred to as V1
•The current for R1 is
referred to as I1
•RT is the total
resistance of the circuit
Sample problem
• Which of the following resistors are
parallel to each other, and which are in
series?
R3
R2
PARALLEL
TO R3
R1
R2 and R3
ARE IN
SERIES
Keeping track of V, I, R
• In all circuits, you are always asking
yourself what the V, I, and R is of each
load in the circuit
• In order to calculate this, you must
understand the basic rules associated
with each type of circuit
• They were developed by a Russian
scientist named Kirchoff and therefore
are known as KIRCHOFF’S LAWS (KL)
KL for voltage in Series Circuits
• Because electrons MUST travel through
each load in the circuit, they have to
give up energy to each one as they do
so
• That means the total energy that an
electron gives up at each load is equal
to what it started with at the start
• VT = V1 + V2 + V3 + …+Vn
Sample question
• In a series circuit, one resistor has a
voltage of 3 V and another has a
voltage of 2 V. What is the total
voltage provided by the battery?
VT
V2
V1
KL for current in a series circuit
• Since a series circuit provides no other
pathway – the current stays constant at
all points
• It is like a single water pipe that has no
back up – the flow of water is the same
at the start as it is in the middle and the
end – since water from the back pushes
water at the front
• IT = I 1 = I 2 = I 3 = … = I 4
Sample problem
• The current leaving a battery that is
connected to a series circuit is
measured as being 5 A. What is the
current moving through the two
resistors in the circuit?
IT
I2
I1
KL for voltage in parallel circuits
• In a parallel circuit, electrons
only have to move through the
loads that are in their paths
• That means that each electron
only has to give up energy to
the load in their path
• Each electron gives up the
same amount of energy
• So the voltage of resistors
parallel to each other are
equal to each other
• VT = V1 = V2 = V3 = … = Vn
IT
I2
I1
Sample problem
• Two parallel resistors are
attached to a battery
providing 9 V of power. What
is the voltage across the two
resistors?
VT
V1
V2
KL law for current in parallel
circuits
• In parallel circuits, electrons
split up
• That means the current splits
up
• If you add up the current in
each path, you will have the
total current of the circuit
• IT = I 1 + I 2 + I3 + … + I n
IT
Sample problem
• A parallel circuit has 2
resistors. If the total current
leaving the battery is 10 A,
and the first resistor has a
current of 2 A, what is the
current in the second resistor?
IT
I1
I2
Kirchoff’s Laws for Resistance
• Using Ohm’s Law and KL for voltage
and current in parallel and series
circuits, the resistance of each type of
circuit can also be analyzed as well
KL for Resistance in Series
Circuits
• In a Series circuit, since:
•
•
•
•
•
VT = V1 + V2 + V3 + …+Vn
And V = IR
Then:
IRT = IR1 + IR2 + IR3 + …+IRn
Therefore: since the I values are the
same, they cancel out on both sides
giving:
• RT = R1 + R2 + R3 + …+Rn
KL for Resistance in Parallel
Circuits
•
•
•
•
•
In a parallel circuit, since:
IT = I 1 + I 2 + I3 + … + I n
And I = V/R, therefore:
V/RT = V/R1 + V/R2 + V/R3 + .. + V/Rn
Since the voltage value is the same in a
parallel circuit, the V’s cancel out on the
RS and LS giving:
• 1/RT = 1/R1 + 1/R2 + 1/R3 + .. + 1/Rn