23 Series and Parallel Circuits

BIGIDEA
Write the Big Idea for this chapter.

Use the “What I Know” column to list the things you know about the Big Idea. Then list the
questions you have about the Big Idea in the “What I Want to Find Out” column. As you read the
chapter, fill in the “What I Learned” column.

K W L
What I Know What I Want to Find Out What I Learned
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Science Notebook • Series and Parallel Circuits

341
23 Series and Parallel Circuits
1 Simple Circuits
MAINIDEA
Write the Main Idea for this lesson.
Series and Parallel Circuits

REVIEW VOCABULARY Recall and write the definition of the Review Vocabulary term.
resistance resistance The opposition offered by a body or substance to
the passage through it of a steady electric current

NEW VOCABULARY Use your book to fill in the term that matches each definition.

circuit in which there are several current paths

circuit in which there is only one path for the current

a series circuit that produces a potential difference source that is less than
the potential difference across the battery

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value of a single resistor that, when it replaces all the resistors in the
circuit, results in the same current

Science Notebook • Series and Parallel Circuits

342
 1 Simple Circuits (continued)
Student Edition, pp. 624–625 Compare Write four statements that compare similarities between a
river and an electrical circuit.

1- both a river and an electric current involve the concept of

flow

2- the size of the current flow in an electrical circuit is related

more to the size of the river than it is to the speed of the river

3- Resistance is a measure of the opposition to current flow in

an electric circuit

GET IT? Define the term series circuit.

Is an electric circuit in which all circuit elements are arranged

in a single path

Draw a picture of a series circuit that contains two resistors. Place one
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.

ammeter between the battery and the first resistor. Place a second
ammeter between the two resistors. Place a third ammeter between the
second resistor and the battery. Label the ammeters to indicate the
current each one measures.

n a series circuit with two resistors and three ammeters, it

would be set up as follows:

A battery symbol (with the positive and negative terminals).

Two resistors (represented by zigzag lines).
Three ammeters (A1, A2, and A3).
Between the battery's positive terminal and the first resistor,
you would place ammeter A1. Label it as "A1" to indicate it
Evaluate
measures If two
theidentical
currentlamps are connected
leaving in series, how does the
the battery.
potential
Between difference
the twoinresistors,
the two lamps compare?
place ammeter A2. Label it as
The potential difference across each lampflowing
"A2" to indicate it measures the current between the
is not equal
resistors.
Between the second resistor and the battery's negative
terminal, place ammeter A3. Label it as "A3" to indicate it
measures the current returning to the battery.

Science Notebook • Series and Parallel Circuits

343
1 Simple Circuits (continued)
Student Edition, pp. 626–627 Write the equation for equivalent resistance for resistors in series, and
explain what it means in your own words.

R eq = R1 + R2 + R3

Explain how you would find the current through a series circuit if you
knew all the resistances and the potential difference of the source.
By adding up the individual resistances of each resistor in the

series

Identify What kind of circuit could you use to produce a 8 V potential

difference from a 12-V battery?

You can use a voltage divider circuit

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Draw Sketch a diagram of a voltage-divider circuit.

Start with a horizontal line to represent the ground (0V) or

the common reference point. Label this line as "0V" or "GND.
"

Draw a battery symbol on the left side of the line to

represent the power source. Label it with the voltage value,
such as "V_battery" or "V."

Connect the positive terminal of the battery to one end of a

zigzag resistor
Summarize symbol (to represent
how a photoresistor changes thea potential
resistor).difference
Label this
in a
resistor
voltage as "R1."
divider.
Voltage
Connectdivider increases
the other end ofwhen the R1
resistor light
tointensity
the inputincreases
of a second
resistor (another zigzag symbol). Label this resistor as "R2."

Connect the other end of resistor R2 to the ground (0V) line.

The point between R1 and R2 where they are connected is

the output
Science of the
Notebook voltage
• Series divider.
and Parallel Label this point as "Vout" or
Circuits
"V_divider." 344

You can use arrows or lines to indicate the direction of

 1 Simple Circuits (continued)
Student Edition, p. 628 TRY IT!
Use with Example Problem 1 Problem
POTENTIAL DIFFERENCE IN A SERIES CIRCUIT Two resistors, 6.0 Ω and
Use this column for 9.0 Ω are connected across a 12-V battery.
scratch work and a. What is the current in the circuit?
sketches.
b. What is the potential difference across each resistor?
c. If you replace the 6.0-Ω resistor with a second 9.0-Ω resistor, will the
current increase, decrease, or remain the same?
d. What is the new potential difference across the first 9.0-Ω resistor?

1. ANALYZE AND SKETCH THE PROBLEM

KNOWNS UNKNOWNS
12 v
∆Vsource = =?
6
R1 = =?
9
R2 = =?

2. SOLVE FOR THE UNKNOWN

a. First determine the equivalent resistance. Then, use the relationship
between current, potential difference, and resistance.
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In a series circuit with two resistors, let's say R1 and R2,

we first find the equivalent resistance by adding the
resistances together: R_eq = R1 + R2. Then, we can use
Ohm's law, which relates current (I), potential difference
(V),the
b. Use and resistance
relationship (R): current, potential difference, and
between
resistance to find the potential difference across each resistor.
V =find
To I*R the potential difference (voltage) across each
resistor in a series circuit, you can use Ohm's law, which
So, thecurrent
relates current(I),
in the circuitdifference
potential can be calculated
(V), and as I=V/
resistance
R_eq,
(R). where V is the applied voltage or potential
c. Repeat the procedure
difference, and R_eq thea.equivalent
fromispart using the new values. This
resistance.
In
The a series
equation circuit
allows
potential uswith two
to find
difference resistors,
the
across eachlet's
current say R1
flowing
resistor and
andR2,
through
(V1 the we
V2) is
first find
entire
given by: the
series equivalent
circuit." resistance by adding the resistances
together: R_eq = R1 + R2. Then, we can use Ohm's law,
which
V1 = I relates
* R1 current (I), potential difference (V), and
resistance
d. Repeat
V2 = I the (R):
procedure
* R2 from part b. using the new values.
To find the potential difference (voltage) across each
V = I * R in a series circuit, you can use Ohm's law, which
Where:
resistor
-relates
V1 andcurrent
V2 are(I),thepotential
potentialdifference
differences across
(V), the first and
and resistance
So,
(R).the current
second resistors,in respectively.
the circuit can be calculated as I = V /
R_eq,
- I is thewhere
currentV isinthe
theapplied
circuit. voltage or potential difference,
and
Science
-The R_eq
Notebook
R1 and is• the
R2 are
potential equivalent
Series resistance.
and Parallel Circuits
the resistances
difference across Thisand
of theresistor
each first equation
andallows
second
(V1 V2) is
us to find the 345
current flowing through the entire series circuit.
resistors,
given by: respectively.
"
1 Simple Circuits (continued)
Student Edition, pp. 630–631 TRY IT! (CONTINUED)
3. EVALUATE THE ANSWER
Yup
• Are the units correct?

Compare a parallel circuit to a waterfall.

A parallel circuit can be compared to a waterfall in terms of the

splitting of current, the total current, and the voltage drop

across each branch

GET IT? Identify the two factors on which the current through a
resistor depends.

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Voltage source and the resistance of the resistor

Consider You have a circuit with three resistors in parallel. You remove
one resistor. What happens to the current through the other resistors?
When you remove one resistor from a circuit with three resistors in parallel, t

Write the equation for equivalent resistance for resistors in parallel, and
explain what it means in your own words.

The equation for the equivalent resistance (R_eq) of

resistors in parallel is given by:

1 / R_eq = 1 / R1 + 1 / R2 + 1 / R3 + ...

In simple terms, the equivalent resistance for resistors in

parallel
Science is found
Notebook by taking
• Series theCircuits
and Parallel reciprocal of the sum of the
reciprocals of the346individual resistances. This equation
reflects the fact that in a parallel configuration, the total
1 Simple Circuits (continued)
Student Edition, pp. 633–634 GET IT? Explain how Kirchhoff’s loop rule and the conservation of
energy are related.
Kirchhoff's loop rule and the conservation of energy are related because Kirc

GET IT? State the loop rule in your own words.

"Kirchhoff's loop rule, also known as the Kirchhoff's Voltage Law (KVL), state

SUMMARIZE
How does the MAINIDEA for this section relate to the chapter’s BIGIDEA?

REVIEW IT!
18. MAINIDEA Compare and contrast the voltages and the currents in series and parallel
circuits.

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In series circuits, the current is the same throughout, and the voltages add up. In parallel circuits, th

19. Total Current A parallel circuit has four branch currents: 120 mA, 250 mA, 380 mA,
and 2.1 A. How much current passes through the power source?
The total current passing through the power source in a parallel circuit is the sum of
the individual branch currents. In this case, it would be:

Total Current = 120 mA + 250 mA + 380 mA + 2.1 A

Total Current = 2.85 A

20. Total Current A series circuit has four resistors. The current through one resistor
is 810 mA. How much current passes through the power source?
So, the total current passing through the power source is 2.85 amperes (A).
810

Science Notebook • Series and Parallel Circuits

348
 1 Simple Circuits (continued)
21. Circuits You connect a switch in series with a 75 W bulb to a 120 V power source.
a. What is the potential b. What is the potential
difference across the switch difference across the switch
when it is closed (turned on)? when it is opened (turned off )?
off Turned on

22. Kirchhoff’s Law’s Compare Kirchhoff’s loop rule to walking around in a loop on the
side of a hill.
you feel like you are going to fall​​

23. Kirchhoff’s Law’s Explain how Kirchhoff’s junction rule relates to the law of
conservation of charge.
Kirchhoff's junction rule, also known as Kirchhoff's current law (KCL), states that the total current en
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.

24. Critical Thinking The circuit in Figure 10 has four identical resistors. Suppose that a
wire is added to connect points A and B. Answer the following questions, and explain
your reasoning.
a. What is the current through the wire?

R R
+
b. What happens to the current through each resistor?
A B
-
R R

c. What happens to the current through the battery?

Figure 10

d. What happens to the potential difference across each

resistor?

Science Notebook • Series and Parallel Circuits

349