Download Parallel Circuits

10.13 Series &
Parallel Circuits
Series Circuits
• electric circuit in which the loads
are arranged one after another in
series.
• A series circuit has only one path
along which electrons can flow.
• If that pathway is
interrupted, the whole circuit
cannot function.
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2
3
Series Circuits
• adding an extra bulb to a series string of
lights makes all the bulbs dimmer.
• electrons use up all their potential difference
going around a series circuit no matter how
many loads are in the circuit. Each load will
use part of the total potential difference,
depending on how much it resists the flow of
electrons.
Series Circuits
• the amount of current is the same in all parts
of a series circuit.
• if more resistors or loads are added, it
will increase the total resistance of the
circuit.
• this decreases the current.
Parallel Circuits
• an electric circuit in which the
loads are arranged so that
electrons can flow along more
than one path.
• the points where a circuit
divides into different paths or
where paths combine are called
junction points
• An interruption or break in one
pathway does not affect the
other pathways in the circuit.
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2
1
Parallel Circuits
• adding a new pathway with
more resistors or loads does not
affect the resistance in any of
the other pathways.
• adding extra resistors or loads
in parallel circuit decreases the
total resistance of the circuit.
Parallel Circuits
• each electron has the same amount of
energy, and electrons must lose all their
energy on the path they are on.
• this is why the potential difference across
parallel resistors will always be the same,
even though the resistors themselves are
different
Parallel Circuits
• since a parallel circuit has
many pathways for current to
flow, the current coming
from the battery is not the
same as the current along
each pathway
• at each junction point, some
electrons go one way while
others go another
Summary of Current, potential difference,
and resistance in series and parallel circuits.
Circuit
Potential Difference
Series
circuit
Each load uses a portion of the
total potential difference supplied
by the battery.
VT = V1 + V2 + V3
Each load uses all the potential
difference supplied by the battery.
VT = V1 = V2 = V3
Parallel
circuit
Circuit
Current
Series
circuit
The current is the same
throughout a series circuit.
Itotal = I1 = I2 = I3
Parallel
circuit
The current divides into different
paths. A pathway with less
resistance will have a greater
current.
Itotal = I1 + I2 + I3
Circuit
Resistance
Series
circuit
The current decreases when
more resistors are added.
RT = R1 + R2 + R3
Adding resistors in parallel
decreases the total resistance
of the circuit.
Parallel
circuit
Sample Question 1:
In Series
1. Consider 2 W and 4 W resistors in
series with a 12 V battery. Assuming
ideal ammeters and voltmeters, what
will be: I1, I2, V1, V2.
Recall: For resistors in series, the total resistance, RT,
is given by: RT = R1 + R2
Solution
•
•
Current, I1
First, calculate the total resistance of circuit:
•
RT = R1 + R2
=2W+4W
=6W
Now use Ohm's law to calculate current:
V= I R
•
•
•
•
•
•
So I = V / R
= 12 V / 6 W
=2A
The current in the wire to the left of the 2 W resistor = 2 A
Current, I2
In a series circuit, the current is always the same, so the current in
the wire to the right of the 4 W resistor is also 2 A.
• Voltage, V1
• Use Ohm's law to calculate voltage across the 2W resistor:
•
V = IR
=2A×2W
=4V
• The voltage V1 = 4 V
• Voltage, V2
• Similarly for the 4W resistor:
•
V = IR
=2A×4W
=8V
• The voltage V2 = 8 V
•
Check:
•
•
VT = V1 + V2
12V = 4V + 8V
Sample Question 2:
In Parallel
Now consider two resistors in parallel with a 6 V
battery. For resistors in parallel, the total
resistance is given by:
Using the values displayed on the graph, calculate
V1, V2, I4, I5.
Solution
• Voltage, V1
• First, calculate the equivalent
resistance of the two resistors:
• 1 / R = 1 / R1 + 1 / R2
= (1 / 3) + (1 / 4)
= (7 / 12) W
• So R = (12 / 7) W
• Now use Ohm's law to calculate voltage V1:
• V1 = I1 × R
= 3.5 A × (12 / 7) W
=6V
• i.e. the battery voltage, V1 = 6 V
• The voltage V1 = 6 V
• Voltage, V2
• Use Ohm's law to calculate voltage across the
4 W resistor:
• V2 = I3 × R2
= 1.5 A × 4 W
=6V
• The voltage V2 = 6 V
• Note that for parallel circuits the voltage is
the same across all resistors.
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•
•
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Current, I4
This must be identical to I3, i.e. 1.5 A
The current I4 = 1.5 A
Current, I5
This must be identical to I1, i.e. 3.5 A
The current I5 = 3.5 A