Series and parallel resistances

1
Series and parallel resistances
2
Series circuits
A series circuit has only one path for the flow
of electric current.
I
I
I
3
Parallel circuits
In a parallel circuit the electric current can
split apart and come back together again.
V
V
4
Series circuits
The battery and the resistors in these circuits
are identical. What is different about these
circuits?
5
Series circuits
The circuit with 3 resistors is 3 times harder
for the current to flow through.
I1
I2
I3
When you add resistors in series, equivalent
resistance increases and current flow decreases
I3 lt I2 lt I1
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Equivalent resistance

• What is equivalent resistance?
• Equivalent resistance is the total combined
  resistance of a group of resistors.
• Equivalent resistance has the value of a single
  resistor that could replace the multiple
  resistors in a circuit, while keeping total
  current through the circuit the same.

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Equivalent resistance
These two circuits have the same total resistance
. . .
. . . so they will have the same total current,
I.
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Equivalent resistance series
For resistors in series, you can find the
equivalent resistance by simply adding up the
individual resistances
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Engaging with the concepts
A 10 O resistor, a 15 O resistor, and a 5 O
resistor are connected in series. What is the
equivalent resistance of this arrangement?


15
10
5
10 O 15 O 5 O 30 O
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Engaging with the concepts
Two strings of tree lights, each with a
resistance of 150 O, are connected together in
series. What is the Req?
150
150
0
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Engaging with the concepts
Two strings of tree lights, each with a
resistance of 150 O, are connected together in
series. What is the Req?
300 O
150
300
150
0
When you add resistors in series does Req
increase or decrease?
Does total current increase or decrease?
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Engaging with the concepts
Two strings of tree lights, each with a
resistance of 150 O, are connected together in
series. What is the Req?
300 O
150
450
150
150
When you add resistors in series does Req
increase or decrease?
Req increases
Does total current increase or decrease?
I decreases
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What is the Req of each circuit?
Req _______
Req _______
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What is the Req of each circuit?
Req 10 O
Req 15 O
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How much current flows?
Req 10 O
Req 15 O
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How much current flows?
1 A
0.67 A
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Parallel circuits
A parallel circuit has more paths for electric
current to flow. The circuit on the right lets
twice as much current flow.
What is the Req for the parallel circuit? R
2R ½ R
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Parallel circuits
In the circuit with parallel resistors total
current flow doubles because total resistance is
halved.
What is the Req for the parallel circuit? R
2R ½ R
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Equivalent resistance parallel
When you add resistors in parallel, total
resistance goes DOWN. To find the Req you must
add the inverse of the resistances
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Equivalent resistance parallel
If you have two 4 O resistors in parallel, what
is the equivalent resistance? A. ½ O
B. 2 O C. 4 O D. 8 O
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Equivalent resistance parallel
Dont forget to flip the fraction at the end!
If you have two 4 O resistors in parallel, what
is the equivalent resistance? A. ½ O
B. 2 O C. 4 O D. 8 O
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Engaging with the concepts
A 10 O resistor and a 15 O resistor are connected
in parallel. What is the Req of this
arrangement?
10
15
Equivalent resistance
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Engaging with the concepts
A 10 O resistor and a 15 O resistor are connected
in parallel. What is the Req of this
arrangement? 6 ohms
10
15
6
Equivalent resistance
When resistors are connected in parallel, total
resistance decreases.
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What is the Req of each circuit?
These are all 10 O resistors. What is the Req in
each case?
Req ____
Req ____
Req ____
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What is the Req of each circuit?
These are all 10 O resistors. What is the Req in
each case?
Req 5 O
Req 10 O
Req 3.3 O
Adding resistors in parallel makes the total
resistance decrease.
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How much current flows?
Apply Ohms law ( V IR ) to find the total
current through the battery.
Req 5 O
Req 10 O
Req 3.3 O
I ____
I ____
I ____
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How much current flows?
Apply Ohms law ( V IR ) to find the total
current through the battery.
Req 5 O
Req 10 O
Req 3.3 O
I 9 A
I 3 A
I 6 A
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Voltage drops resistors in series
Half as much current flows in the series
circuit. What are the voltage drops across the
two resistors in series?
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Voltage drops resistors in series
10 V drop
10 V drop
Resistor in series
Single resistor
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Voltage drops resistors in parallel
Twice as much current flows in the parallel
circuit. What are the voltage drops across the
resistors in parallel?
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Voltage drops resistors in parallel
4 A
4 A
20 V drop
Single resistor
Resistor in parallel
Each resistor in parallel has the full 20 V drop.
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Assessment

• Two resistors with resistances of 10 O and 30 O
  are connected in series with a 20 volt battery.
• What is the equivalent resistance of the circuit?

1. What is the current flow through the circuit?

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Assessment

• Two resistors with resistances of 10 O and 30 O
  are connected in series with a 20 volt battery.
• What is the equivalent resistance of the circuit?

1. What is the current flow through the circuit?

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Assessment

• Two resistors with resistances of 10 O and 30 O
  are connected in series with a 20 volt battery.
• What is the equivalent resistance of the circuit?

1. What is the current flow through the circuit?

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Assessment

• Two resistors with resistances of 10 O and 30 O
  are connected in parallel with a 20 volt battery.
• What is the equivalent resistance of the circuit?
• b) What is the current flow through the circuit?

36
Assessment

• Two resistors with resistances of 10 O and 30 O
  are connected in parallel with a 20 volt battery.
• What is the equivalent resistance of the circuit?
  7.5 O
• b) What is the current flow through the circuit?

37
Assessment

• Two resistors with resistances of 10 O and 30 O
  are connected in parallel with a 20 volt battery.
• What is the equivalent resistance of the circuit?
  7.5 O
• b) What is the current flow through the circuit?

38
Assessment

1. If you connect these two identical resistors as
   shown, will they together draw more or less
   current than one of the resistors alone?

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Assessment

1. If you connect these two identical resistors as
   shown, will they together draw more or less
   current than one of the resistors alone?

They will draw more current, because they are
connected in parallel. There are now two
different, but identical paths for electricity to
flow, so the current doubles!
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Celebrations of learning

• pg. 497 1-5 ?